很急的機率問題，拜託高手指點！
2014-04-14 6:02 am
In a game, a participant is given three attempts to hit a ball. On each try, she either scores a hit, H, or a miss, M. The game requires that the player must alternate which hand she uses in successive attempts. That is, if she makes her first attempt with her right hand, she must use her left hand for the second attempt and her right hand for the third. Her chance of scoring a hit with her right hand is .7 and with her left hand is .4. Assume that the results of successive attempts are independent and that she wins the game if she scores at least two hits in a row. If she makes her first attempt with her right hand, what is the probability that she wins the game?
回答 (10)
2014-04-15 10:07 am
✔ 最佳答案
In the first and third attempts :P(hit) = 0.7
P(miss) = 1 - 0.7 = 0.3
In the second attempt :
P(hit) = 0.4
P(miss) = 1 - 0.4 = 0.6
P(win the game)
= P(at least two hits in a row)
= P(three hits) + P(two hits in a row)
= P(hit, hit, hit) + P(hit, hit, miss) + P(miss, hit, hit)
= 0.7 x 0.4 x 0.7 + 0.7 x 0.4 x 0.3 + 0.3 x 0.4 x 0.7
= 0.196 + 0.084 + 0.084
= 0.364
2014-04-15 02:08:31 補充：
in a row 是連續的意思。
參考: 賣女孩的火柴, 賣女孩的火柴
2014-05-08 4:05 pm
2014-05-04 5:24 pm
2014-05-02 3:19 pm
2014-05-01 5:09 pm
2014-04-28 3:45 pm
2014-04-28 6:44 am
2014-04-24 1:38 pm
2014-04-14 10:58 pm
我想 "at least two hits in a row" 應是指 "連續兩次hits"
0.7x0.4 + 0.3x0.4x0.7 = 0.364
0.7x0.4 + 0.3x0.4x0.7 = 0.364
2014-04-14 6:17 pm
收錄日期: 2021-04-13 21:18:14
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140413000015KK06493