   Chapter 14.4, Problem 24E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONExpected Number Consider families with three children, and assume that the probability of having a girl is 1 2 .(a) Complete the table for the probabilities of having 0, 1, 2, or 3 girls in a family of three children.(b) Find the expected number of girls in a family of three children. Number of girls Probability 0 1 8 1 2 3

To determine

(a)

The table for the probabilities of having 0, 1, 2, or 3 girls in a family of three children.

Explanation

Given:

The probability of having a girl is 12.

Approach:

The expression for probability is given as,

P=C(n,r)pr(1p)nr ...(1)

Here, P is the required probability and r successes in n independent trials of the experiment.

Calculation:

Calculate the probability of having 1 girl.

Substitute 12 for p, 1 for r and 3 for n in equation (1), to calculate the probability.

P(1)=C(3,1)(12)1(112)31=3(12)(14)=38

Calculate the probability of having 2 girl.

Substitute 12 for p, 2 for r and 3 for n in equation (1), to calculate the probability.

P(2)=C(3,2)(12)2(112)32=3(14)(12)=38

Calculate the probability of having 3 girl

To determine

(b)

The expected number of girls.

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