Question

Brian rolls a fair dice 60 times.
How many times would Brian expect to roll a three?

Answer 1

10 times.

Explanation:

He rolls all the dice independently, so The expected number of 3's is 60 * (expected number of 3's in one throw).

The expected number of 3's in one throw is:

5/6 * 0 + 1/6 * 1 = 1/6

because 5/6 of the time we roll zero 3's and 1/6 of the time we roll one 3 :D

So he should expect (60 * 1/6 = 10) 3's in 60 throws.