+2653 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?
+1926 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! :)
