Two different numbers are chosen at random from the set {1, 2, 3, ..., 5}. What is the probability that the product of the numbers is even?

LiIIiam0216 Jun 29, 2024

#1**+1 **

There are many ways to solve this problem, but I prefer casework.

There are two cases.

The first case is that we get two even numbers from the lists. We have

\(\frac{\binom22}{\binom52} = 1/10\)

The second case we have is that we one odd number and we have one even number. Using permutations, we get

\(\frac{\binom31}{\binom52} = 6/10\)

Adding these two together, we get

\(1/10+6/10=7/10\)

So our final answer is 0.7

Thanks! :)

NotThatSmart Jun 29, 2024