The problem asks for the probability that the product of two numbers, one drawn from each box, is an even number.

Analyzing Number Properties

First, let's list the numbers in each box and identify whether they are odd or even.

Calculating Total Outcomes

The total number of possible outcomes is the product of the number of chips in each box.

Total Outcomes = (Chips in Box 1) $\times$ (Chips in Box 2) = $5 \times 5 = 25$.

Probability of an Odd Product

The product of two numbers is odd only if both numbers are odd. It's often easier to calculate the probability of the complementary event (product being odd) and subtract it from 1.

• The probability of drawing an odd number from Box 1 is $P(\text{Odd}_1) = \frac{\text{Number of odd chips in Box 1}}{\text{Total chips in Box 1}} = \frac{3}{5}$.
• The probability of drawing an odd number from Box 2 is $P(\text{Odd}_2) = \frac{\text{Number of odd chips in Box 2}}{\text{Total chips in Box 2}} = \frac{2}{5}$.
• The probability that both drawn numbers are odd (resulting in an odd product) is: $P(\text{Odd Product}) = P(\text{Odd}_1) \times P(\text{Odd}_2) = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}$.

Probability of an Even Product

The probability of the product being even is 1 minus the probability of the product being odd.

$P(\text{Even Product}) = 1 - P(\text{Odd Product})$

$P(\text{Even Product}) = 1 - \frac{6}{25} = \frac{25}{25} - \frac{6}{25} = \frac{19}{25}$.

Conclusion

The probability for the product to be an even number is $\frac{19}{25}$.