Question (Probability)

Augustus

2009-01-17 8:50 am

Dick is playing a shooting game. In the first trial, the probability of shooting down the target and missing the target are equally likely. For the coming trials, the probability of shooting down a target depends on his previous shooting result. After a successful shot, the probability of a successful shot in his next trial is 3/5. After a failed trial, the probability of a successful shot in his next trial is 1/4.
Consider Dick's first three trials only, find the probability that he misses once.

回答 (1)

老爺子

2009-01-17 10:10 am

✔ 最佳答案

P(He misses once)
= P(fail, success, success) + P(success, fail, success) + P(success, success, fail)
= (1/2) x (1/4) x (3/5) + (1/2) x (1 - 3/5) x (1/4) + (1/2) x (3/5) x (1 - 3/5)
= (3/40) + (1/20) + (3/25)
= 49/200
=

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