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A radio station has a contest in which contestants roll a regular 6-sided die. If he...

A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything.

What is the probability that out of the first 5 contestants exactly 2 win $100?

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Answer #1

Probability to win $100 = Probability to rolls a 3 or a 4 = 2/6 = 1/3

Let X be the number of contestants out of 5 that roll 3 or a 4 (or win $100). Then X ~ Binomial(n = 5, p = 1/3)

Probability that out of the first 5 contestants exactly 2 win $100 = P(X = 2)

= 5C2 * (1/3)2 * (2/3)3

= 10 * (1/3)2 * (2/3)3

= 0.3292181

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