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, which allows us to find the probability of an event based on prior knowledge of conditions related to the event.

### Step-by-step Solution:

1. **Define Events**:
- Let \( C_1 \): the event that the chosen coin is the two-headed coin.
- Let \( C_2 \): the event that the chosen coin is the biased coin (75% heads).
- Let \( C_3 \): the event that the chosen coin is the unbiased coin (50% heads).
...