Solution Found!
Consider a coin that comes up heads with probability P and
Chapter , Problem 40(choose chapter or problem)
Consider a coin that comes up heads with probability P and tails with probability 1 - p. Let qn be the probability that after n independent tosses, there have been an even number of heads. Derive a recursion that relates qn to qn-I, and solve this recursion to establish the formula qn = (1 + (1 - 2Pt) /2.
Questions & Answers
QUESTION:
Consider a coin that comes up heads with probability P and tails with probability 1 - p. Let qn be the probability that after n independent tosses, there have been an even number of heads. Derive a recursion that relates qn to qn-I, and solve this recursion to establish the formula qn = (1 + (1 - 2Pt) /2.
ANSWER:Step 1 of 2
Assume that
A: Event that initialtosses produce an even number of heads.
E: Event that thetoss results in a head
Obtaining an even number of head in n tosses is possible in two distinct ways:
Case1: The firsttosses results in an even number of heads, and the text, that is, the toss results in tails: this the event
Case2: The firsttosses results in an odd number of heads, and the text, that is, the toss results in heads: this the event
Again, A and E are the independent events, where