We are given a probability problem where two balls are selected at random, one after the other, with replacement. We need to find the probability that both balls are red. However, we are missing information about the number of red balls and the total number of balls. Let's assume the problem means that 5 out of 12 balls are red. We will solve it with that assumption.

1. Problem Description

We are given a probability problem where two balls are selected at random, one after the other, with replacement. We need to find the probability that both balls are red. However, we are missing information about the number of red balls and the total number of balls. Let's assume the problem means that 5 out of 12 balls are red. We will solve it with that assumption.

2. Solution Steps

Let $R$ be the event of selecting a red ball.

The probability of selecting a red ball on the first draw is $P(R_1) = \frac{5}{12}$.

Since the ball is replaced, the total number of balls and the number of red balls remain the same for the second draw.

Therefore, the probability of selecting a red ball on the second draw is $P(R_2) = \frac{5}{12}$.

Since the two events are independent, the probability of selecting two red balls is the product of the individual probabilities:

$P(R_1 \text{ and } R_2) = P(R_1) \times P(R_2) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144}$.

3. Final Answer

The probability that both balls are red is $\frac{25}{144}$.

The answer is A.