Question

A fair 6-sided die is rolled 4 times. What is the probability of rolling exactly three prime numbers?

Answer 1

`1/16`

Explanation:

We have 4 independent events that we can multiply the probabilities together.

The prime numbers on a 6-sided cube are `2, 3, 5` and so that's 3 values. Which means that `P("roll is prime")=3/6=1/2` for each roll.

This also means that to roll a non-prime number, the probability is `1-1/2=1/2`

So we can say:

`1/2xx1/2xx1/2xx1/2=1/16`, or slightly less than `10%`