Three urns contain 6 red, 4 black 4 red, 6 black and 5 red, 5 black balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the first urn.

Explanation

To solve the problem step by step, we will use Bayes' theorem to find the probability that the red ball drawn came from the first urn.

### Step 1: Define the events
Let:
- \( U_1 \): the event that the ball is drawn from urn 1.
- \( U_2 \): the event that the ball is drawn from urn 2.
- \( U_3 \): the event that the ball is drawn from urn 3.
- \( R \): the event that the ball drawn is red.
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