Question

What is the probability that both numbers chosen by a random number generator from 1 through 40 are even?

Answer 1

To find the probability that both numbers chosen by a random number generator from 1 through 40 are even, we first need to determine the total number of even numbers in the range from 1 to 40.

The even numbers between 1 and 40 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, and 40. There are 20 even numbers in total.

Next, we also consider the total number of choices available when selecting two numbers from the set of numbers 1 through 40. Since the range consists of numbers from 1 to 40, there are 40 possible choices for each number.

Thus, the total number of ways to choose 2 numbers from 40 is given by:

\[
40 \times 40 = 1600
\]

Now, we find the number of successful outcomes where both chosen numbers are even. Since there are 20 even numbers, the number of ways to choose 2 even numbers is:

\[
20 \times 20 = 400
\]

Finally, the probability \( P \) that both numbers chosen are even is the ratio of the number of successful outcomes to the total number of outcomes:

\[
P = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{400}{1600} = \frac{1}{4}
\]

Thus, the probability that both numbers chosen are even is:

\[
\boxed{\frac{1}{4}}
\]