Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of rock, paper, and scissors every round (making independent selections each round). Each round can end in a win, loss, or a tie for each player.

a. What is the probability Ann wins the first round. (Remember that a tie is a possibility)

Prob=

b. What is the probability that Ann's first win happens in round #5?

Prob=

C. What is the probability that Ann's first win comes after round #5?

Prob=

Question

Mathematics

Alvaro Collier

22 January, 14:03

Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of rock, paper, and scissors every round (making independent selections each round). Each round can end in a win, loss, or a tie for each player.

a. What is the probability Ann wins the first round. (Remember that a tie is a possibility)

Prob=

b. What is the probability that Ann's first win happens in round #5?

Prob=

C. What is the probability that Ann's first win comes after round #5?

Prob=

+1

Answers (1)

Know the Answer?

Isabela Bruce · Answer 1

a) 1/3

b) 0.0658436214

Step-by-step explanation:

Part a

Ann wins first round = (P, R) + (S, P) + (R, S) = 3 possibilities of win

Total outcomes = Wins + Losses + Ties = 9 possibilities

Hence,

P (Ann wins first round) = 3/9 = 1/3

Part b

Ann losses or ties first 4 rounds and wins 5th round

P (Ann loosing or tie in any round) = 6/9 = 2/3

Hence,

P (Ann wins 5th round only) = (2/3) ^4 * (1/3) = 0.0658436214

Part c