What would the value of x be in the given scenario? When rolling a die 20 times, what is the probability of rolling exactly a 4 six times.

Question

 I've been struggling on this question and just need explanation on how to get the answer

Answer 1

Let p = probability of rolling a 4 on a single roll = 1/6

     q = probability of not rolling a 4 on a single roll = 5/6

 

Then P(6 rolls of 4 out of 20 rolls) = ₂₀C₄(p)⁴(q)^20-4

 

                                                            ⁼ 4845(1/6)⁴(5/6)¹⁶ ≈ 0.2022