A bag contains 3 red and 7black balls. Two balls are selected at random one by one without replacement. If the second ball happens to be red, what is the probability that the first selected ball is also red?

Explanation

To solve the problem, we need to find the probability that the first selected ball is red given that the second ball is red. We can use Bayes' theorem for this calculation.

### Step-by-Step Solution:

1. **Define Events:**
- Let \( A \) be the event that the first ball is red.
- Let \( B \) be the event that the second ball is red.

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