Math 4510 Midterm 2 1. (17 points) When three friends go for coffee, they decide
ID: 3370495 • Letter: M
Question
Math 4510 Midterm 2 1. (17 points) When three friends go for coffee, they decide who will pay the having each person flip a coin and then having the "odd person out" pay. Aips produce the same result (and thus no "odd person out"), then they make a second check by If all three round of flips and continue to do so until there is an odd person out. For ezample, f the flips were (H, H, T), then person 3 pays, whereas if the flips where (T, H,7), person 2 pays. I the flips are (H, H, H) or (T, T,T), they flip coins again. What is the probability that more than 2 rounds are needed?Explanation / Answer
The probability that more than 2 rounds needed
= P[in the first round the output is (HHH) or (TTT)] + P[in the second round the output is (HHH) or (TTT)]
= P[HHH] + P[TTT] + P[HHH] + P[TTT]
= 1/8 + 1/8 + 1/8 + 1/8 = 1/2