# Thread: Determine the probability of the product of two numbers being even.

1. ## Determine the probability of the product of two numbers being even.

Well, the title says it all. Assume that the probability of choosing an odd number and an even number is the same.

I thought I would split it into cases: one number is even, both numbers are even, and neither number is even. I get this:

(1/2) + (1/4) - (1/4), respectively.

So is 1/2 correct?

Thanks! Any help is appreciated!

2. ## Re: Determine the probability of the product of two numbers being even.

The product of two numbers are even if at least one number is even. Hence I get an answer of $\displaystyle \dfrac{3}{4}$

3. ## Re: Determine the probability of the product of two numbers being even.

The four possibilities are

Odd * Odd
Odd * Even
Even * Odd
Even * Even

3 favorable cases out of 4. Hence the probability is 3/4

4. ## Re: Determine the probability of the product of two numbers being even.

Originally Posted by gpksam07
The four possibilities are

Odd * Odd
Odd * Even
Even * Odd
Even * Even

3 favorable cases out of 4. Hence the probability is 3/4
I did $\displaystyle 1 - P(OO)$ where P(OO) is the chance of two odd numbers.