Ben rolls four fair 10-sided dice. What is the probability that exactly three of the dice show a prime number?
The prime numbers from 1-10: 2, 3, 5, and 7.
This means a 2/5 chance of rolling a prime number on 1 die. Thus, three dice have an 8/125 chance of rolling all prime numbers.
The chance that 1 die doesn't roll a prime number is 3/5, which comes from 1-2/5. This gives a 24/625 chance for one arrangement of dice rolls (i.e. PPPN). To find the total number of arrangements, we do 4 choose 3 = 4. Since there are 4 different ways to obtain this result, our answer is multiplied by 4 to get 96/625.