Question

An experiment consists of flipping a weighted coin with Pr[H]=0.8Pr[H]=0.8. The experiment ends when either heads is flipped 3 times or tails is flipped. What is the probability that heads was flipped at least once given the coin was flipped at most two times?

Answer 1

Given that the coin was flipped at most two times, there are only 2 possible ways that this can happen:

• T, that is the first toss is a tail and we stop, P(T) = 1 - P(H) = 1 - 0.8 = 0.2
• HT, that is first heads and then toss, P(HT) = 0.8*0.2 = 0.16

Now given that coin was flipped at most two times, probability that heads was flipped at least once is computed using bayes theorem here as:
= P(HT) / [P(HT) + P(T)]
= 0.16/0.36
= 0.4444

Therefore 0.4444 is the required probability here.