A box contains 4 green apples and 6 red apples. You take out one apple at random, then put it back and take out another apple at random. What is the probability that both apples you took out were green?
The probability of both apples being green is 4/25.

Here's the reasoning:

1. When you take out the first apple, there are 4 green apples and 6 red apples, making a total of 10 apples.
2. The probability of picking a green apple on your first try is 4/10 (4 green apples out of 10 total apples).
3. Since you put the apple back after taking it out, there are still 4 green apples and 6 red apples in the box when you pick the second apple.
4. The probability of picking a green apple on your second try is also 4/10.
5. To find the probability of both events happening together (picking two green apples), we multiply their individual probabilities: (4/10) * (4/10) = 16/100, which simplifies to 4/25.

So, the probability of both apples being green is 4/25.