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. Student A and B are playing rock-scissor-paper. What is the probability that A wins two...

. Student A and B are playing rock-scissor-paper. What is the probability that A wins two times in a roll from the beginning? (Assume both players play rock, scissor or paper purely randomly.)

Student A and B are playing rock-scissor-paper. What is the probability that A wins two times in a roll within the first 3 rounds played? (Assume both players play rock, scissor or paper purely randomly.)

Math   Statistics-And-Probability   
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Answer #1

A player who decides to play rock will beat another player who has chosen scissors ("rock crushes scissors" or sometimes "blunts scissors"), but will lose to one who has played paper("paper covers rock"); a play of paper will lose to a play of scissors ("scissors cuts paper").

Each player has 3 options to choose from

Hence there is a total of 3*3=9 combinations

if B chooses Scissor then A can win if it chooses rock.

If B chooses paper then A can win if it chooses scissor.

If B chooses rock then A can win if it chooses paper.

Hence out of 9 possibilities A can win in 3.

Hence the probability that A can win in one round is

the probability that A wins two times in a roll within the first 3 rounds played =

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