Three fair dice are rolled. Let the random variable X be the number of die that are showing a roll of 1. Complete the probability distribution table. (Give probabilites to three decimals)

Question

x P(X=x)

0

1

2

3

Answer 1

On any one die, the probability of 1 is 1/6 and the probability of not 1 is 5/6

The three dice are independent so the probabilities combine in the binomial way:

P(n ones) = ₃C_n Pⁿ(1-P)^3-n where P is 1/6 and the coefficient is the combination of 3 things n at a time.

I'll do one for you: P(one 1 ) = ₃C₁ (1/6)(5/6)² the coefficient is 3

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