Three men toss coins to see who pays for coffee If all three

Three men toss coins to see who pays for coffee. If all three match, they toss again, Otherwise the \"odd man\" pays for coffee. What is the probability that they will need to do this more than once? What is probability of tossing at most twice?

Solution

The Prob[ need to toss more than once ] = Prob [getting all three same ] = P (HHH) + P(TTT) = 0.125 + 0.125 = 0.25

Prob [tossing at most twice] = P [ all three match ]* P [all three do not match ] = 0.25 * 0.75 = 0.1875