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

$\frac{1}{16}$

#### 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 $P \left(\text{roll is prime}\right) = \frac{3}{6} = \frac{1}{2}$ for each roll.

This also means that to roll a non-prime number, the probability is $1 - \frac{1}{2} = \frac{1}{2}$

So we can say:

$\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{16}$, or slightly less than 10%