Question

Rework problem 7 from section 3.4 of your text, involving the selection of a colored ball from one of three bowls. Assume that you randomly pick one of the bowls: X, Y, or Z. You then randomly draw one ball out of the selected bowl and note its color. The bowls contain the following colored balls: Bowl X: 2 red, 2 white, and 3 blue. Bowl Y: 2 red, 1 white, and 1 blue. Bowl Z: 1 red, 3 white, and 2 blue. (1) If the ball is blue, what is the probability that it was drawn from bowl X? (2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y?

Answer 1

Answer:

• Question (1): 1/2 = 0.5

• Question (2): 1/6 ≈ 0. 17

Explanation:

1. Arrange the information of the balls contained in the bowls in a table:

                       Bowl X      Bowl Y       Bowl Z     Total

Red balls              2               2                1               5

White balls           2                1                3              6

Blue balls             3                1                2              6

                           ==============================

Totals                     7                4              6             17  

2. To answer each question use the basic definition of probabilities

• Probability = # of favorable events / # of possible events

3. Question (1) If the ball is blue, what is the probability that it was drawn from bowl X?

• Number of total blue balls: 6

• Number of blue balls in the bowl X: 3

• Probability that a ball that is blue was drawn from the bowl X: P (b/X)

       P (b/X) = number of blue balls in the bowl X / total number of blue balls = 3 / 6 = 1/2 = 0.5

       

4. Question (2) If the ball is either blue or white, what is the probability that it was drawn from bowl Y?

• Number of total blue and white balls: 6 + 6 = 12

• Number of blue balls and white balls in the bowl Y: 1 + 1 = 2

• Probability that a ball that is either blue or white was drawn from the bowl Y: P (b or w / Y)

       P (b or w /Y) = number of blue balls and white balls in the bowl Y / total number of blue balls and white balls = 2 / 12 = 1/6 ≈ 0.17