A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

Step-by-step solution

Let H denote head and T denote tail. The sample space for the experiment is S = H, TH, TTH, TTT . The condition given is that head does not appear on the first toss. This means the first toss is T . The subset of the sample space where the first toss is T is A = TH, TTH, TTT . The event that the coin is tossed thrice is B = TTH, TTT . We are looking for the conditional probability P(B|A) = P(B A) P(A) . Since B A , B A = B . The probabilities of the outcomes are: P(TH) = 1 2 1 2 = 1 4 P(TTH) = 1 2 1 2 1 2 = 1 8 P(T