A fair die will be rolled 9 times. What is the probability that 4, 5, or 6 is rolled exactly 2 times? Round your answer to four decimal places.

Probability (4,5 or 6) exactly 2 outcomes = 6/54 or 0.1111

Step-by-step explanation:

Probability of the die to have, 4, = 1/6

Probability of the die to have, 5, = 1/6

Probability of the die to have, 6, = 1/6

It is rolled 9 times

Probability that 4 is rolled 2 times out of 9 outcomes = 2/9

Probability that 5 is rolled 2 times out of 9 outcomes = 2/9

Probability that 6 is rolled 2 times out of 9 outcomes = 2/9

Probability of the die to have 4 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

Probability of the die to have 5 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

Probability of the die to have 6 in 2 outcomes of 9 rolls = 1/6 * 2/9 = 2/54

Probability that 4,5, or 6 is rolled exactly two times = 2/54+2/54+2/54 = 6/54 = 0.1111