Question

A coin is tossed repeatedly; on each toss, a head is shown with probability p or a tail with probability 1 − p. All tosses are independent. Let E denote the event that the first run of r successive heads occurs earlier than the first run of s successive tails. Let A denote the outcome of the first toss. Show that P(E|A=head)=pr−1 +(1−pr−1)P(E|A=tail). Find a similar expression for P (E | A = tail) and then find P (E).

Answer 1

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