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 i

Explanation

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

### Step 1: Define Events
Let:
- \( E_1 \): Event of choosing the two-headed coin
- \( E_2 \): Event of choosing the biased coin (75% heads)
- \( E_3 \): Event of choosing the unbiased coin (50% heads)
- \( A \): Event of tossing a coin and getting heads
...