Bernoulli trials refer to independent trials each with success probability p and failure probability 1-p.
Let P(n) be the probability when there is an even number of successes in n Bernoulli trials.
Show that
P(n)=p ( 1-P(n-1) ) + ( 1-p )P(n-1) for n larger and =1
Please answer with explanation, thx!
Probability hardness
2010-02-19 12:30 am
回答 (1)
2010-02-19 1:00 am
✔ 最佳答案
Case 1: If the last trial is success (probability p), then the previous n-1 trials should consist a odd number of successes which has probability 1-P(n-1)Case 2: If the last trial is fail (probability 1-p), then the previous n-1 trials should consist an even number of successes which has probability P(n-1)
Combines Case 1 and 2
P(n)=p ( 1-P(n-1) ) + ( 1-p )P(n-1) for n >=1
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