Question

Refer to Example 4.40. An urn contains six red balls, six white balls, and six blue balls, and sample of four balls is drawn at random without replacement.

Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)

b) An urn contains eight red balls, eight white balls, and eight blue balls, and sample of five balls is drawn at random without replacement.

Compute the probability that the sample contains at least one ball of each color. (Round your answer to four decimal places.)

Answer 1

ANSWER

a)

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

Total number of balls = 6+6+6 = 18

Number of selections possible = 18C4 = 3,060

Number of ways in which 4 red balls can be selected from 6 = 6C4 = 15

Number of ways in which 4 white balls can be selected from 6 = 6C4 = 15

Number of ways in which 4 blue balls can be selected from 6 = 6C4 = 15

P(all of the balls in the sample are the same color) = (15+15+15)/3060

= 0.0147