Question

An urn has 11 balls that are identical except that 3 are white and 8 are red. A sample of 4 is selected randomly without replacement. What is the probability that exactly 2 are white and 2 are red?

Answer 1

The probability of selecting exactly 2 white balls and 2 red balls from the urn is 14/55 or approximately 0.255.

Step-by-step explanation:

To find the probability of selecting exactly 2 white balls and 2 red balls from the urn, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

1. First, let's calculate the number of favorable outcomes. There are 3 ways to choose 2 white balls out of the 3 white balls in the urn, and there are 8 ways to choose 2 red balls out of the 8 red balls in the urn. So, the number of favorable outcomes is (3 choose 2) * (8 choose 2) = 3 * 28 = 84.
2. Next, let's calculate the total number of possible outcomes. Since we are selecting 4 balls without replacement, the total number of possible outcomes is (11 choose 4) = 330.
3. Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. The probability of selecting exactly 2 white balls and 2 red balls is 84/330 = 14/55, which is approximately 0.255.