The probability of drawing a red ball can be found by the formula of total probability:
Example 2. There are three urns identical in appearance. The first urn contains 24 green balls, the second urn contains 12 green and 12 red balls, and the third urn contains 24 red balls. We draw a green ball from a randomly selected urn. Find the probability of the ball being drawn from the first urn.
Solution. Assume that are the hypotheses consisting in selecting the first, the second and the third urn respectively. Let A be the event of drawing a green ball. Since the selection of any of the urns is equally likely then
.
It is clear that the probability of drawing a green ball from the first urn is ; the probability of drawing a green ball from the second urn is the probability of drawing a green ball from the third urn is .
Therefore, the desired probability (i.e. the probability of the green ball being drawn from the first urn) can found from Bayes’ formula
Example 3. There are two boxes. The first box contains 8 blue and 7 red balls, the second, 4 blue and 6 red balls. We draw one ball from the second box and place it into the first one, then we randomly draw one ball from the first box.
