Question

Asked Apr 29, 2019

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An urn contains seven red balls, seven white balls, and seven blue balls and a sample of five balls is drawn at random without replacement.

a. Compute the probability that the sample contains four balls of one color and one of another color

b. compute the probability that all of the balls in the sample space are the same color

c. Compute the probability that the sample contains at least one ball of each color

Step 1

Given total red balls = 7

Total white balls = 7

Total blue balls = 7

A sample of five balls is drawn at random without replacement.

we need probability that we get four balls of one colour and one ball of another colour.

Total number of balls in urn = 7+7+7 = 21

The total number of ways of picking five balls from 21 balls = ^{21}C_{5}

First we need to pick one colour from three three colours = ^{3}C_{1}

Number of ways of selecting four balls of one colour = ^{7}C_{4}

Number of ways of selecting one colour from remaining two colours = ^{2}C_{1}

Number of ways of selecting one ball from that colour = ^{7}C_{1}

So number of ways of selecting five balls with four of one colour and one of different colour is calculated as shown below. Its probability = 0.0722

Step 2

The total number of ways of selecting five balls from 21 balls = 21C5

The number of ways of selecting one colour = 3C1

The total number of ways of selecting five balls from 7 balls = 7C5

The total number of choosing five balls of one colour = &n...

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