Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was fair coin?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that the coin was fair given that we tossed it and got a head.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( E_1 \) be the event that the fair coin is chosen.
- Let \( E_2 \) be the event that the two-headed coin is chosen.
- Let \( H \) be the event that a head is obtained when the coin is tossed.
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