Question

A fair die is rolled 8 times.

a. what is the probability that the die comes up 6 exactly twice?

Answer 1

P(first 2 rolls = 6 and rest not 6) = 1/6 * 1/6 * (5/6)^6 = 0.00930272

there are 8C2 ways of obtaining exactly 2 6's in 8 throws = 28 ways

so required probability is 0.00930272 * 28 = 0.26 to nearest hundredth