Ben rolls 5 fair 12-sided dice. the 12 faces of each die are numbered from 1 to 12. what is the probability that exactly two of the dice show an even number?

We will use the Binomial Probability formula to find the answer

The formula is given by ⁿCₓ (p) ˣ (1-p) ⁿ⁻ˣ

Where:

n, the number of trials = 5

x, the number of success that we aim = 2

p, the probability of success = 0.5 ⇒ there are six out of twelve numbers on the dice that are even

Substitute these values into the formula, we have

P (2) = ⁵C₂ (0.5) ² (1-0.5) ⁵⁻²

P (2) = ⁵C₂ (0.5) ² (0.5) ³

P (2) = 0.3125