Question

 

A dice is flipped twelve times. What is the probability that less than two fives appear?

Answer 1

The probability of flipping a five is ⅙, so the probability of not flipping a five is ⅚.

The probability of no fives at all is (⅚)¹².

The probability of only one five is 12(⅚)¹¹(⅙) because the single five can come first, second, third, etc., but nowhere else.

So the probability of less than 2 fives is the sum of no-fives and one-five:

(⅚)¹²+12(⅚)¹¹(⅙)=(⅚)¹¹(⅚+2)=0.3813 or about 38.13%.