Question

You have 20 blue balls and 13 red balls in a bag. You put your hand in and remove 2 at a time. If theyre of the same color, you add a blue ball to the bag. If theyre of different colors, you add a red ball to the bag. Assume you have a big supply of blue & red balls for this purpose.

Answer 1

The probability of drawing two blue balls is 7/16.

Initially, there are 20 blue balls and 13 red balls in the bag.

After the first draw, there are 19 blue balls and 13 red balls remaining.

If the first two balls drawn are both blue, you add a blue ball to the bag, resulting in 20 blue balls and 13 red balls.

If the first two balls drawn are different colors, you add a red ball to the bag, resulting in 19 blue balls and 14 red balls.

The probability of drawing two blue balls is 20/33 * 19/32 = 15/64.

The probability of drawing two different colored balls is 33/32 * 13/31 = 13/64.

Since the events are mutually exclusive, the probability of either event occurring is the sum of their probabilities: 15/64 + 13/64 = 28/64 = 7/16.