Question

A bucket contains six white balls and five red balls. A sample of four balls is selected

at random from the bucket, without replacement. What is the probability that the
sample contains...
Exactly two white balls and two red balls?
At least two white balls?/

Answer 1

The probability of getting at least two white balls = (15*10 + 20 + 15)/330 = 65/330 or approximately 0.1969.

Explanation:

To find the probability of selecting balls, we need to use combinations.

Total number of ways to select 4 balls out of 11 = C(11,4) = 330

1. Probability of getting exactly two white balls and two red balls:

Number of ways to select 2 white balls out of 6 = C(6,2) = 15

Number of ways to select 2 red balls out of 5 = C(5,2) = 10

Number of ways to combine these selections = 15 * 10 = 150

Therefore, the probability of getting exactly two white balls and two red balls = 150/330 = 5/11 or approximately 0.4545.

2. Probability of getting at least two white balls:

Number of ways to select 2 white balls out of 6 = C(6,2) = 15

Number of ways to select 2 balls out of 5 that are not white = C(5,2) = 10

Number of ways to select 3 white balls out of 6 = C(6,3) = 20

Number of ways to select 4 white balls out of 6 = C(6,4) = 15

Therefore, the probability of getting at least two white balls = (15*10 + 20 + 15)/330 = 65/330 or approximately 0.1969.