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avatar+1981 

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?

 Jun 29, 2024
 #1
avatar+1252 
+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! :)

 Jun 29, 2024

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