Question

Find the probability of throwing at most 2 sixes in 5 throws of single die.

Answer 1

Let X be a random variable that denotes the number sixes in 6 throws of a single die. Then, X can take value 0,1,2,3,4,5 and 6.

Here, p = probability of throwing six in a single throw = 1/6 and q = probability of not throwing six in a single throw = 1-p = 1-1/6 = 5/6

Clearly, X follows binomial distribution with  parameters n = 6, p = 1/6 q = 5/6.