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

### Step 1: Define the Events
Let:
- \( C_1 \): Event that the two-headed coin is chosen.
- \( C_2 \): Event that the biased coin is chosen.
- \( C_3 \): Event that the unbiased coin is chosen.
- \( H \): Event that the outcome of the toss is heads.
...