Question

You are playing rock, paper, scissors (RPS) with a friend. Because you are good at predicting your friend’s strategy, there is a 60% chance each time that you play her, that you win. You play 7 games of rock, paper scissors with your friend and would like to know how many of them you win. Use this information to answer the following questions.

1.What is the probability that you win exactly three of the seven games played? (To four decimal places)

2.What is the probability that you win five or fewer games? (To four decimal places)

Answer 1

Let X be the random variable denoting the number of games you win out of 7 games.

So X follows a binomial distribution with parameters

n= 7

p = 0.6

1.the probability that you win exactly three of the seven games played

P(X = 3)

= 0.1935

2.probability that you win five or fewer games

= 1 - [ P(X = 6) + P(X = 7)]

= 1 - [ 0.1306368 + 0.0279936 ]

= 0.8414

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