There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that the coin chosen was the two-headed coin given that the result of the toss was heads.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( E_1 \): Event that the chosen coin is the two-headed coin.
- Let \( E_2 \): Event that the chosen coin is the biased coin.
- Let \( E_3 \): Event that the chosen coin is the unbiased coin.
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