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**Statistics and Probability**

Rock, Paper, Scissors: A Probability Experiment

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Rock, paper, Scissors In the game rock, paper, scissors two players have to show either scissors, paper, or rock using their hands as follows: rock paper scissors The rules of the game are that: Scissors beats paper (it cuts). Paper beats rock (it wraps). Rock beats scissors (it breaks). If both players show the same hands it is a draw.

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Rock, paper, scissors What is the probability that both players will show the same hands in a game of rock, paper, scissors? We can list all the possible outcomes in a two-way table using S for Scissors, P for Paper and R for Rock. Scissors Paper Stone First player Second player SS SS SP SR PS PP PP PR RS RP RR TT 3 9 = 1 3 P(same hands) =

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Rock, paper, scissors What is the probability that the first player will win a game of rock, paper, scissors? Using the two-way table we can identify all the ways that the first player can win. Scissors Paper Stone First player Second player SS SP SR PS PP PT TS RP RR SP PR Remember the rules of the game: Scissors beats paper; paper beats stone; stone beats scissors. RS 3 9 = 1 3 P(first player wins) =

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Rock, paper, scissors What is the probability that the second player will win a game of rock, paper, scissors? Using the two-way table we can identify all the ways that the second player can win. Scissors Paper Stone First player Second player SS SP ST PS PP PR RS TP RR SR PS Remember the rules of the game: Scissors beats paper; paper beats stone; stone beats scissors. RP 3 9 = 1 3 P(second player wins) =

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**Rock, paper, scissors Is rock, paper, scissors a fair game? 1**

P(first player wins) = 1 3 P(second player wins) = 1 3 P(a draw) = 1 3 Both player are equally likely to win so, yes, it is a fair game. Review what is meant by a fair game. In a fair game all players are equally likely to win. Allow pupils to play the game in pairs and to record their results. Discuss the fact that in 30 games we would expect to get 10 wins for the first player, 10 wins for the second player and 10 draws. Discuss why this does not happen in reality. Play rock paper scissors 30 times with a partner. Record the number of wins for each player and the number of draws. Are the results as you expected?

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Mathematical Expectation. A friend offers you the chance to play the following game: You bet $2 and roll a die. If you roll a 6 you win $5 plus your bet.

Mathematical Expectation. A friend offers you the chance to play the following game: You bet $2 and roll a die. If you roll a 6 you win $5 plus your bet.

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