Версия для печати темы

Автор: wsnet 7.3.2007, 8:47

Два игрока A и B поочередно бросают монету. Выигравшим считается тот, у кого раньше выпадет герб. Первый бросок делает игрок A, второй – B, третий – A и т.д.
1. Найти вероятность того, что выиграл A не позднее k-го броска.
2. Каковы вероятности выигрыша для каждого игрока при сколь угодно длительной игре?
k=4


Вроде все просто. Но не могу понять как ее решать

Автор: нонна 7.3.2007, 8:59

1. вероятность выпадения герба 0,5. решки-тоже 0,5. по формуле бернулли находим р4(1).
2. событие равновероятно, поэтому вероятность 0,5.

Автор: venja 7.3.2007, 15:16

Как раз все не так просто.
Кстати, в первом задании есть неоднозначность истолкования: Найти вероятность того, что выиграл A не позднее 4-го броска (к=4) - похоже надо считать все броски (и А и В) - так я и буду считать (а может быть надо считать только броски А?).
Обозначим события:
А1 - в первом броске выпал орел,
А2 - во втором броске выпал орел,
.
.
.
Ак - в к-м броске выпал орел,.....
Понятно, что вероятности всех этих событий =1/2.

1. Пусть событие С - выиграл A не позднее 4-го броска.
Тогда С=А1+(неА1)*(неА2)*А3 (первое слагаемое означает, что А выиграл на первом броске, а второе, что на третьем (после того, как кинул В), а на 4-м А никак выиграть не может, так как в моем толковании условия четные броски делает только В, а нечетные только А).
Тогда Р(С)=Р(А1+(неА1)*(неА2)*А3 )=(1/2)+(1/2)^3= 5/8.

2. Каковы вероятности выигрыша для каждого игрока при сколь угодно длительной игре?

Пусть событие С - игрок А выиграл (при сколь угодно длительной игре). Тогда
С=А1+(неА1)*(неА2)*А3 +(неА1)*(неА2)*(неА3)*(неА4)*А5+.... .
Точно также, как и ранее (используя несовместность слагаемых и независимость сомножителей):
Р(С)=(1/2)+(1/2)^3 +(1/2)^5+....=2/3 (сумма беск. геом. прогр.).
Тогда вероятность выигрыша для В (при сколь угодно длинной игре)=1-2/3=1/3.
Вроде так.
Расчеты лучше проверить.

Автор: Black Ghost 7.3.2007, 18:50

В 1-й задаче скорее всего 4 броска делает каждый (я думаю, что если A выигрывает только на 3-м броске (если считать броски и A, и , то зачем тогда говорить "не позднее 4-го" - это же вроде как меньше или РАВНО 4-х бросков... Зачем тогда равно, если считать все броски? Хотя может это просто для того, чтобы запутать ...

Тогда тут прямо можно использовать формулу
С=А1+(неА1)*(неА2)*А3 +(неА1)*(неА2)*(неА3)*(неА4)*А5...

Если задуматься, то шансов выиграть у первого игрока больше (хотя бы даже на первом шаге), чем у второго, потому что шансы второго игрока напрямую зависят от результатов первого.

Автор: venja 7.3.2007, 19:10

Я тоже сначала именно так и подумал, и даже решение записал для этого случая из тех же соображений. Но потом посмотрел на строчку из условия задачи:
Первый бросок делает игрок A, второй – B, третий – A и т.д..
Видите, как идет нумерация бросков?
Поэтому переделал, хотя тот же нюанс смущает: "Зачем тогда равно, если считать все броски?".

Автор: Black Ghost 7.3.2007, 20:34

"Первый бросок делает игрок A, второй – B, третий – A и т.д.."
Перечитал... Что-то не обратил внимание сначала. Теперь не могу не согласиться, что нужно считать общее количество...
Интересно всё же спросить автора этой задачи, что он имеет в виду на самом деле и зачем тогда даёт такое странное условие - включая равенство четырём

Автор: A_nn 8.3.2007, 4:43

Думаю, что просто в данном варианте 4. А у других - другие k... Не мог же автор давать одни нечетные числа . Правда, мог спросить вероятность того, что А не проиграет до k-го броска .

Автор: wsnet 9.3.2007, 6:09

Всем большое спасибо за помощь

Автор: chocolet1 28.11.2022, 7:33

https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-nefertari-vivi/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-flame-emperor-sabo/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-portgas-d-ace/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-hiep-si-cua-bien-jinbe/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-soul-king-brook/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-nguoi-sat-franky/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-nico-robin/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-tony-tony-chopper/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-usopp/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-mieu-tac-nami/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-hac-cuoc-sanji/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-roronoa-zoro/ https://gz-zjrq.com/gioi-thieu-ve-nhan-vat-monkey-d-luffy/ https://www.ilanda.info/ https://www.ilanda.info/content/page2.php https://www.ilanda.info/in/songoku.html https://www.ilanda.info/in/songohan.html https://www.ilanda.info/in/piccolo.html https://www.ilanda.info/in/vegeta.html https://www.ilanda.info/in/bulma.html https://www.ilanda.info/in/krilin.html https://www.ilanda.info/in/chichi.html https://www.ilanda.info/in/songoten.html https://www.ilanda.info/in/vuthienlaosu.html https://www.ilanda.info/in/trunks.html https://www.ilanda.info/in/yamcha.html https://www.ilanda.info/in/chiaotzu.html https://www.ilanda.info/in/yajirobe.html https://www.ilanda.info/in/so17.html https://www.ilanda.info/in/majinbuu.html https://www.ilanda.info/in/so18.html https://www.ilanda.info/in/santa.html https://www.ilanda.info/in/videl.html https://www.ilanda.info/in/tienshinhan.html https://www.ilanda.info/in/pan.html https://gilport.com/ https://ronaldo.vin/ https://arzimasks.com/ https://arzimasks.com/nhan-vat/ https://arzimasks.com/nhan-vat/page/2/ https://arzimasks.com/nhan-vat/page/3/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-kawamura/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-kuntakku/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-kataoka-tamao/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-mii-chan/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-miyoko-mangetsu/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-nobisaku/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-sunekichi-honekawa/ https://arzimasks.com/195-2/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-sunetsugu-honekawa/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-sunetsugu-honekawa/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-ba-noi-nobita/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-me-jaian/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-bo-suneo/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-me-suneo/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-tanaka-yasuo/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-minamoto-michiko/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-minamoto-yoshio/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-sewashi/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-jaiko/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-nobisuke/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-nobi-nobiro/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-eiichiro-senjou/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-dekisugi/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-tamako-nobi/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-nobi-nobisuke/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-dorami/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-suneo/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-jaien/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-shizuka/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-nobita/ https://arzimasks.com/gioi-thieu-ve-nhan-vat-doraemon/ https://londonsburning.org/ https://londonsburning.org/nhan-vat/ https://londonsburning.org/nhan-vat/ https://londonsburning.org/nhan-vat/page/3/ https://londonsburning.org/nhan-vat/page/4/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-pikachu/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-shigeru-okido/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-marina/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kenta/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-koharu/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-goh/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-mamane/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-suiren/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-mao/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kaki/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-lillie/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-meowth/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-musashi/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kojiro/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-junsa/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-joy/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-hanako/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-okido/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-yurika/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-serena/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-dento/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-iris/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-hikari/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-masato/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-haruka/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kenji/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-takeshi/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kasumi/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-satoshi/ https://outdoorpark.net/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-conan-edogawa/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-ran-mouri/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-kogoro-mouri/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-ai-haibara/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-yusaku-kudo/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-yukiko-kudo/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-heiji-hattori/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-hiroshi-agasa/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-juzo-megure/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-gin/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-eri-kisaki/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-vermouth/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-ninzaburo-shiratori/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-kiyonaga-matsumoto/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-kazunobu-chiba/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-miwako-sato/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-wataru-takagi/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-yumi-miyamoto/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-ayumi-yoshida/ https://outdoorpark.net/gioi-thieu-ve-nhan-vat-heizo-hattori/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-hanako/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-okido/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-yurika/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-serena/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-dento/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-iris/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-hikari/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-masato/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-haruka/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kenji/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-takeshi/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-kasumi/ https://londonsburning.org/gioi-thieu-ve-nhan-vat-satoshi/ https://soakcitycp.com/ https://soakcitycp.com/nhan-vat/ https://soakcitycp.com/nhan-vat/page/2/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-evergreen/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-freed-justine/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-laxus-dreyar/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-makarov-dreyar/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-levy-macgarden/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-lisanna-strauss/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-elfman-strauss/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-mirajane-strauss/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-cana-alberona/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-gildarts-clive/ https://soakcitycp.com/nhan-vat/page/3/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-panther-lily/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-gajeel-redfox/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-juvia-lockser/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-carla/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-wendy-marvell/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-erza-scarlet/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-gray-fullbuster/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-lucy-heartfilia/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-happy/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-natsu-dragneel/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-mystogan/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-porlyusica/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-mavis-vermillion/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-yuri-dreyar/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-mest-gryder/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-macao-conbolt/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-romeo-conbolt/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-alzack-connell/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-bisca-connell/ https://soakcitycp.com/gioi-thieu-ve-nhan-vat-asuka-connell/ https://dual-web.info/ https://dual-web.info/nhan-vat/ https://dual-web.info/nhan-vat/page/2/ https://dual-web.info/nhan-vat/page/3/ https://dual-web.info/gioi-thieu-ve-nhan-vat-saitama/ https://dual-web.info/gioi-thieu-ve-nhan-vat-genos/ https://dual-web.info/gioi-thieu-ve-nhan-vat-tatsumaki/ https://dual-web.info/gioi-thieu-ve-nhan-vat-silver-fang/ https://dual-web.info/gioi-thieu-ve-nhan-vat-atomic-samurai/ https://dual-web.info/gioi-thieu-ve-nhan-vat-garou/ https://dual-web.info/gioi-thieu-ve-nhan-vat-king/ https://dual-web.info/gioi-thieu-ve-nhan-vat-zombieman/ https://dual-web.info/gioi-thieu-ve-nhan-vat-drive-knight/ https://dual-web.info/gioi-thieu-ve-nhan-vat-pig-god/ https://dual-web.info/gioi-thieu-ve-nhan-vat-superalloy-darkshine/ https://dual-web.info/gioi-thieu-ve-nhan-vat-watchdog-man/ https://dual-web.info/gioi-thieu-ve-nhan-vat-flashy-flash/ https://dual-web.info/gioi-thieu-ve-nhan-vat-metal-bat/ https://dual-web.info/gioi-thieu-ve-nhan-vat-tank-top-master/ https://dual-web.info/gioi-thieu-ve-nhan-vat-puri-puri-prisoner/ https://dual-web.info/gioi-thieu-ve-nhan-vat-blast/ https://dual-web.info/gioi-thieu-ve-nhan-vat-laian/ https://dual-web.info/gioi-thieu-ve-nhan-vat-okamatachi/ https://dual-web.info/gioi-thieu-ve-nhan-vat-bushidrill/ https://dual-web.info/gioi-thieu-ve-nhan-vat-heavy-tank-loincloth/ https://dual-web.info/gioi-thieu-ve-nhan-vat-death-gatling/ https://dual-web.info/gioi-thieu-ve-nhan-vat-stinger/ https://dual-web.info/gioi-thieu-ve-nhan-vat-smile-man/ https://dual-web.info/gioi-thieu-ve-nhan-vat-fubuki/ https://dual-web.info/gioi-thieu-ve-nhan-vat-gun-gun/ https://dual-web.info/gioi-thieu-ve-nhan-vat-shooter/ https://dual-web.info/gioi-thieu-ve-nhan-vat-genus/ https://dual-web.info/gioi-thieu-ve-nhan-vat-mumen-rider/ https://dual-web.info/gioi-thieu-ve-nhan-vat-onsoku-no-sonic/ http://trabzondershanesi.com/ http://trabzondershanesi.com/nhan-vat/ http://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-urie-kuki/ http://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-nashiro-yasuhisa/ http://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-tsukiyama-shuu/ http://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-banjo-kazuichi/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-omori-yakumo/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-noro/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-tatara/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kurona-yasuhisa/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-ippei-kusaba/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-yoriko-kosaka/ https://trabzondershanesi.com/nhan-vat/page/2/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-ryoko-fueguchi/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-hisashi-ogura/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-enji-koma/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-enji-koma/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-arima-kisho/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kaya-irimi/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kimi-nishino/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kirishima-ayato/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kureo-mado/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-uta/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-shinohara-yukinori/ https://trabzondershanesi.com/nhan-vat/page/3/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-suzuya-juuzou/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-renji-yomo/

https://tsumemiko.com/nhan-vat/page/2/ https://tsumemiko.com/nhan-vat/page/3/ https://tsumemiko.com/nhan-vat/page/4/ https://haarpstatusnetwork.com/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kurosaki-ichigo/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kuchiki-rukia/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-inoue-orihime/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-sado-yasutora/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-ishida-uryu/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-isshin-kurosaki/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kisuke-urahara/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-shihouin-yoruichi/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-shigekuni-yamamoto/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-hitsugaya-toshiro/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-aizen-sosuke/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-jushiro-ukitake/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kenpachi-zaraki/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kuchiki-byakuya/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-komamura-sajin/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-komamura-sajin/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-shunsui-kyoraku/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-soifon/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-rangiku-matsumoto/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-mayuri-kurotsuchi/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-shinji-hirako/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-kensei-muguruma/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-yadomaru-lisa/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-izuru-kira/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-yachiru-kusajishi/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-madarame-ikkaku/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-ichimaru-gin/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-yumichika-ayasegawa/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-nanao-ise/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-ulquiorra-cifer/ https://haarpstatusnetwork.com/gioi-thieu-ve-nhan-vat-grimmjow-jaegerjaquez/ https://haarpstatusnetwork.com/nhan-vat/ https://haarpstatusnetwork.com/nhan-vat/page/2/ https://haarpstatusnetwork.com/nhan-vat/page/3/ https://haarpstatusnetwork.com/nhan-vat/page/4/ https://superlambbanana.com/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-eren-yeager/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-mikasa-ackerman/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-armin-arlert/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-annie-leonhart/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-levi-ackerman/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-hange-zoe/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-erwin-smith/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-ymir-fritz/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-reiner-braun/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-jean-kirschtein/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-connie-springer/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-sasha-blouse/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-floch-forster/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-bertholdt-hoover/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-zeke-yeager/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-pieck-finger/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-porco-galliard/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-gabi-braun/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-historia-reiss/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-eren-kruger/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-ymir/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-marco-bodt/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-willy-tybur/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-kenny-ackerman/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-lara-tybur/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-uri-reiss/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-azumabito-kiyomi/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-mike-zacharias/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-moblit-berner/ https://superlambbanana.com/gioi-thieu-ve-nhan-vat-frieda-reiss/ https://superlambbanana.com/nhan-vat/ https://superlambbanana.com/nhan-vat/page/2/ https://superlambbanana.com/nhan-vat/page/2/ https://superlambbanana.com/nhan-vat/page/4/ https://wan2o.com/ https://wan2o.com/gioi-thieu-ve-nhan-vat-midoriya-izuku/ https://wan2o.com/gioi-thieu-ve-nhan-vat-bakugo-katsuki/ https://wan2o.com/gioi-thieu-ve-nhan-vat-todoroki-shoto/ https://wan2o.com/gioi-thieu-ve-nhan-vat-uraraka-ochaco/ https://wan2o.com/gioi-thieu-ve-nhan-vat-toshinori-yagi/ https://wan2o.com/gioi-thieu-ve-nhan-vat-shota-aizawa/ https://wan2o.com/gioi-thieu-ve-nhan-vat-shigaraki-tomura/ https://wan2o.com/gioi-thieu-ve-nhan-vat-kirishima-eijiro/ https://wan2o.com/gioi-thieu-ve-nhan-vat-hado-nejire/ https://wan2o.com/gioi-thieu-ve-nhan-vat-kaminari-denki/ https://wan2o.com/gioi-thieu-ve-nhan-vat-asui-tsuyu/ https://wan2o.com/gioi-thieu-ve-nhan-vat-tenya-lida/ https://wan2o.com/gioi-thieu-ve-nhan-vat-toga-himiko/ https://wan2o.com/gioi-thieu-ve-nhan-vat-mineta-minoru/ https://wan2o.com/gioi-thieu-ve-nhan-vat-yaoyorozu-momo/ https://wan2o.com/gioi-thieu-ve-nhan-vat-ashido-mina/ https://wan2o.com/gioi-thieu-ve-nhan-vat-jiro-kyoka/ https://wan2o.com/gioi-thieu-ve-nhan-vat-toru-hagakure/ https://wan2o.com/gioi-thieu-ve-nhan-vat-mt-lady/ https://wan2o.com/gioi-thieu-ve-nhan-vat-mirio-togata/ https://wan2o.com/gioi-thieu-ve-nhan-vat-all-for-one/ https://wan2o.com/gioi-thieu-ve-nhan-vat-kai-chisaki/ https://wan2o.com/gioi-thieu-ve-nhan-vat-hitoshi-shino/ https://wan2o.com/gioi-thieu-ve-nhan-vat-dabi/ https://wan2o.com/gioi-thieu-ve-nhan-vat-fumikage-tokoyami/ https://wan2o.com/gioi-thieu-ve-nhan-vat-enji-todoroki/ https://wan2o.com/gioi-thieu-ve-nhan-vat-mei-hatsume/ https://wan2o.com/gioi-thieu-ve-nhan-vat-mezou-shouji/ https://wan2o.com/gioi-thieu-ve-nhan-vat-chizome-akaguro/ https://wan2o.com/gioi-thieu-ve-nhan-vat-hizashi-yamada/ https://wan2o.com/nhan-vat/ https://wan2o.com/nhan-vat/page/2/ https://wan2o.com/nhan-vat/page/3/ https://wan2o.com/nhan-vat/page/4/ http://danadrug.com/ http://teamdautu.com/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-akihiro-kanou/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-nishio-nishiki/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-hideyoshi-nagachika/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-rize-kamishiro/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-hinami-fueguchi/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-touka-kirishima/ https://trabzondershanesi.com/gioi-thieu-ve-nhan-vat-kaneki-ken/ https://elliotthester.com/ https://elliotthester.com/nhan-vat/ https://elliotthester.com/nhan-vat/page/2/ https://elliotthester.com/nhan-vat/page/3/ https://elliotthester.com/nhan-vat/page/4/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-meliodas/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-elizabeth-liones/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-hawk/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-diane/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-ban/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-king/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-gowther/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-merlin/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-escanor/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-gilthunder/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-dreyfus/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-hendriksen/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-zaratras/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-griamor/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-gustav/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-zeldirs/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-estarossa/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-hauser/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-guila/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-jericho/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-galand/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-fraudrin/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-melascula/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-grayroad/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-gloxinia/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-gloxinia/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-derieri/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-monspeet/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-drole/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-ludociel/ https://elliotthester.com/gioi-thieu-ve-nhan-vat-jenna/ https://gilport.com/ https://gilport.com/gioi-thieu-ve-nhan-vat-uzumaki-naruto/ https://gilport.com/gioi-thieu-ve-nhan-vat-uchiha-sasuke/ https://gilport.com/gioi-thieu-ve-nhan-vat-hatake-kakashi/ https://gilport.com/gioi-thieu-ve-nhan-vat-jiraiya/ https://gilport.com/gioi-thieu-ve-nhan-vat-gaara/ https://gilport.com/gioi-thieu-ve-nhan-vat-might-gai/ https://gilport.com/gioi-thieu-ve-nhan-vat-killer-bee/ https://gilport.com/gioi-thieu-ve-nhan-vat-tsunade/ https://gilport.com/gioi-thieu-ve-nhan-vat-uzumaki-nagato/ https://gilport.com/gioi-thieu-ve-nhan-vat-nara-shikamaru/ https://gilport.com/gioi-thieu-ve-nhan-vat-mamikaze-minato/ https://gilport.com/gioi-thieu-ve-nhan-vat-hashirama-senju/ https://gilport.com/gioi-thieu-ve-nhan-vat-tobirama-senju/ https://gilport.com/gioi-thieu-ve-nhan-vat-sarutobi-hizuzen/ https://gilport.com/gioi-thieu-ve-nhan-vat-otsutsuki-hagoromo/ https://gilport.com/gioi-thieu-ve-nhan-vat-orochimaru/ https://gilport.com/gioi-thieu-ve-nhan-vat-uchiha-madara/ https://gilport.com/gioi-thieu-ve-nhan-vat-hyuga-hinata/ https://gilport.com/gioi-thieu-ve-nhan-vat-uchiha-itachi/ https://gilport.com/gioi-thieu-ve-nhan-vat-uchiha-obito/ https://gilport.com/gioi-thieu-ve-nhan-vat-haruno-sakura/ https://gilport.com/gioi-thieu-ve-nhan-vat-haruno-sakura/ https://gilport.com/gioi-thieu-ve-nhan-vat-hyuga-neji/ https://gilport.com/gioi-thieu-ve-nhan-vat-rock-lee/ https://gilport.com/gioi-thieu-ve-nhan-vat-inuzuka-kiba/ https://gilport.com/gioi-thieu-ve-nhan-vat-aburame-shino/ https://gilport.com/gioi-thieu-ve-nhan-vat-akimichi-choji/ https://gilport.com/gioi-thieu-ve-nhan-vat-sai-yamanaka/ https://gilport.com/gioi-thieu-ve-nhan-vat-tenten/ https://gilport.com/gioi-thieu-ve-nhan-vat-yamanaka-ino/ https://gilport.com/nhan-vat/ https://gilport.com/nhan-vat/page/2/ https://gilport.com/nhan-vat/page/3/ https://gilport.com/nhan-vat/page/4/ https://tsumemiko.com/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kamado-tanjirou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kamado-nezuko/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-agatsuma-zenitsu/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-hashibira-inosuke/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-tsuyuri-kanao/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-shinazugawa-genya/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-ubuyashiki-kagaya/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-tomioka-giyuu/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-rengoku-kyoujurou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kochou-shinobu/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-uzui-tengen/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-tokitou-muichirou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kanroji-mitsuri/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-shinazugawa-sanemi/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-himejima-gyoumei/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-urokodaki-sakonji/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kuwajima-jigorou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-rengoku-shinjurou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kochou-kanae/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kibutsuji-muzan/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-tamayo/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-yushirou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-kokushibou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-hantengu/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-akaza/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-douma/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-gyokko/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-gyuutarou/ https://tsumemiko.com/gioi-thieu-ve-nhan-vat-daki/ https://tsumemiko.com/nhan-vat/ https://tsumemiko.com/nhan-vat/page/2/

https://tintucmoi24h.today/https://tintucmoi24h.today/page/2/https://tintucmoi24h.today/page/3/https://tintucmoi24h.today/page/4/https://tintucmoi24h.today/page/5/https://tintucmoi24h.today/page/6/https://tintucmoi24h.today/page/7/https://tintucmoi24h.today/page/8/https://tintucmoi24h.today/page/9/https://tintucmoi24h.today/page/10/https://tintucmoi24h.today/page/11/https://tintucmoi24h.today/page/12/https://tintucmoi24h.today/page/13/https://tintucmoi24h.today/page/14/https://tintucmoi24h.today/page/15/https://tintucmoi24h.today/page/16/https://tintucmoi24h.today/page/17/https://tintucmoi24h.today/page/18/https://tintucmoi24h.today/anh-ay-dung-bong-da-de-xay-cau-cho-ke-thu/https://tintucmoi24h.today/quy-do-troi-noi-gap-quy-giang-tran/https://tintucmoi24h.today/nhin-anh-chua-giang-tran-toi-rung-rung-truoc-ronaldo-dinh-cao/https://tintucmoi24h.today/niem-tin-da-mat/https://tintucmoi24h.today/helan-horton-doi-mu-manchester-city-6-3-de-danh-bai-manchester-united/https://tintucmoi24h.today/tansha-to-chuc-hoi-nghi-ket-noi-mo-cua/https://tintucmoi24h.today/haaland-can-su-giup-do-tu-cac-cau-thu-messi-co-the-tu-lam/https://tintucmoi24h.today/ten-hag-chung-toi-da-mat-niem-tin/https://tintucmoi24h.today/barcelona-xac-nhan-de-jongdepay-chan-thuong/https://tintucmoi24h.today/maguire-cac-phuong-tien-truyen-thong-thich-cuong-dieu/https://tintucmoi24h.today/chi-so-cua-cristiano-ronaldo-37-lan-cham-4-lan-sut-3-duong-chuyen-chinh/https://tintucmoi24h.today/2-cu-sut-2-ban-thang-va-1-pha-kien-tao-chinh-dalot-la-nguoi-ghi-diem-cao-nhat/https://tintucmoi24h.today/paris-chao-mung-nguoi-mo-ty-so-champions-league/https://tintucmoi24h.today/sau-khi-messi-ra-di-vi-cuu-tinh-cua-barcelona-da-xuat-hien/https://tintucmoi24h.today/nguoi-ham-mo-phat-cuong-sau-tran-thang-dam-cua-doi-ukraine/https://tintucmoi24h.today/huangjia-stand-%ef%bd%9c-tai-sao-cau-thu-bong-da-the-gioi-ukraine-bi-troi-tay/https://tintucmoi24h.today/doi-truong-doi-tuyen-ba-lan-deo-bang-doi-truong-doi-tuyen-ukraine-tai-world-cup/https://tintucmoi24h.today/doi-mong-du-liverpool-that-bai-nhuc-nha/https://tintucmoi24h.today/voi-viec-bi-cat-giam-90-luong-ban-van-san-sang-lam-viec-chu/https://tintucmoi24h.today/khong-co-su-tha-thu-sau-su-phan-boi-real-madrid-se-khong-bao-gio-ky-hop-dong-voi-mbappe-nua/https://tintucmoi24h.today/lewandowski-lap-cu-dup-lien-tiep-tao-nen-ky-tich-hiem-co-o-la-liga-sau-11-nam/https://tintucmoi24h.today/chinh-thuc-barcelona-ky-hop-dong-voi-chelsea-wings-trong-mot-nam-voi-dieu-khoan-giai-phong-50-trieu-euro/https://tintucmoi24h.today/aubameyang-chia-tay-barcelona-6-thang-giong-nhu-6-nam-xin-gui-loi-cam-on-den-dai-gia-dinh-nay/https://tintucmoi24h.today/chinh-thuc-marcelo-cua-real-madrid-gia-nhap-cuong-quoc-hy-lap-hai-ben-ky-hop-dong-mot-nam/https://tintucmoi24h.today/la-liga-lewandowski-ghi-ban-rafinha-ghi-ban-barcelona-danh-bai-sevilla-3-0/https://tintucmoi24h.today/la-liga-venesius-rodrigo-ghi-ban-real-madrid-2-1-betis-gianh-4-chien-thang-lien-tiep/