A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2 while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair?

Explanation

To solve the problem, we need to find the probability that the coin drawn is fair given that the first toss resulted in heads and the second toss resulted in tails. We will use Bayes' theorem to find this probability.

### Step-by-Step Solution:

1. **Define the Events**:
- Let \( E_1 \) be the event that a fair coin is drawn.
- Let \( E_2 \) be the event that a biased coin is drawn.
- Let \( A \) be the event that the first toss is heads and the second toss is tails.
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