Question

box contains five while balls, four red balls and three blue balls. Suppose that three balls are randomly selected. a. What is the probability that exactly two of the balls are white ? b. What is the probability that one ball of each color is selected ? c. What is the probability that all three of the selected balls have the same color ?

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Number of white balls = 5

Number of red balls = 4

Number if blue balls = 3

Probability = required outcome / Total possible outcomes

Total possible outcomes (Total number of balls) = 5 + 4 + 3 = 12

a. What is the probability that exactly two of the balls are white?

(White, white, not white) or (not white, white, white) or (white, not white, white)

Assume balls were picked without replacement ;

P(white, white, not white) = (5/12 × 4/11 × 7/10) = 0.1060606

P(not white, white, white) = (7/12 × 5/11 × 4/10) = 0.1060606

P(white, not white, white) = (5/12 × 7/11 × 4/10) = 0.1060606

P(exactly 2 white balls) = 3×(0.1060606) = 0.3181818

b. What is the probability that one ball of each color is selected ?

(White, red, blue) or (red, white, blue) or (red, blue, white) or (blue, red, white), (white, blue, red), (blue, white, red)

P(white, red, blue) = (5/12 * 4/11 * 3/10) = 0.0454545

(0.0454545 × 3) = 0.272727

c. What is the probability that all three of the selected balls have the same color ?

P(white, white, white) or P(blue, blue, blue) or P(red, red, red)

P(white, white, white) = (5/12 * 4/11 * 3/10) = 0.0454545

P(blue, blue, blue) = (3/12 * 2/11 * 1/10) = 0.0045454

P(red, red, red) = (4/12 * 3/11 * 2/10) = 0.0181818

(0.0454545 + 0.0045454 + 0.0181818) = 0.0681817