Let's reason through this problem:

1. We know that there are 3 red apples and 5 green apples in the basket.
2. The total number of apples in the basket is 3 + 5 = 8.
3. To find the probability of picking two red apples without replacement, we need to consider the probability of picking the first red apple and then the second red apple.
4. The probability of picking the first red apple is 3/8 (since there are 3 red apples out of 8 total apples).
5. After picking the first red apple, there are now 2 red apples and 7 total apples left in the basket.
6. The probability of picking the second red apple is 2/7.
7. To find the overall probability of picking two red apples, we multiply the probabilities from steps 4 and 6: (3/8) * (2/7) = 6/56.

So, the probability of picking two red apples without replacement is 6/56, which simplifies to 3/28.
There are 3 red apples and 5 green apples in a basket. If you pick two apples at random without replacement, what is the probability that both apples are red?