1. (la , uats) When thre friends go for coffee, they decide who will pay the che

Question

1. (la , uats) When thre friends go for coffee, they decide who will pay the check by If all three having each person flip a coin and then having the "odd person out" pay. Hips produce the same result (and thus no "odd person out"), then they make a second round of flips and continue to do so until there is an odd person out. For ezample, if 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

Sample space for flipping of 3 coins:

(H,H,H),(H,H,T),(H,T,H),(T,H,H),(T,T,H),(H,T,T),(T,H,T),(T,T,T)

For more than 2 rounds to take place, the first two rounds should have any two{(H,H,H) or (T,T,T)} of the 8 possible outcomes.

Thus, probability to make a second round of flip = 2/8

and probability that the person is decided = 6/8

Thus, probability that more than 2 rounds are needed

= 1 - { P(1 round is needed) + P(2 rounds are needed) }

= 1 -{ (6/8) + (2/8)×(6/8) }

= 1/16 = 0.0625

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