Question

suppose we are drawing balls from an urn. the urn contains 30 white balls, 20 green balls, 10 red balls, and 40 yellow balls. if 10 balls are drawn with replacement, what is the probability there are exactly 2 white balls in teh sample of 10 balls?

Answer 1

The probability of drawing exactly 2 white balls from a sample of 10 balls drawn with replacement can be calculated using the binomial probability formula.

Step-by-step explanation:

To find the probability of drawing exactly 2 white balls from a sample of 10 balls drawn with replacement from an urn containing 30 white balls, 20 green balls, 10 red balls, and 40 yellow balls, we can use the binomial probability formula.

1. First, we calculate the probability of drawing a white ball: P(white) = number of white balls / number of total balls = 30 / (30 + 20 + 10 + 40) = 30 / 100 = 0.3
2. Next, we plug in the values into the binomial probability formula: P(exactly 2 white balls) = C(10, 2) * (0.3)^(2) * (1 - 0.3)^(10-2), where C(10, 2) represents the number of ways to choose 2 white balls from 10 balls drawn.
3. Calculating C(10, 2): C(10, 2) = 10! / (2! * (10 - 2)!) = (10 * 9) / 2 = 45.
4. Plugging in the values: P(exactly 2 white balls) = 45 * (0.3)^(2) * (0.7)^(8) ≈ 0.233.