   Chapter 14.2, Problem 41E ### 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

# Four Siblings A couple intends to have four children. Assume that having a boy and having a girl are equally likely events.(a) List the sample space of this experiment.(b) Find the probability that the couple will have only boys.(c) Find the probability that the couple will have two boys and two girls.(d) Find the probability that the couple will have four children of the same gender.(e) Find the probability that the couple will have at least two girls.

To determine

(a)

To find:

The sample space.

Explanation

Given:

A couple intends to have four children. Assume that having a boy and having a girl are equally likely events.

Approach:

Equally likely events are events that have the same probability of occurring.

Calculation:

If there are four girls then there is only one possibility, that is, {GGGG}.

If there are three girls and one boy then there are four possibilities, that is, {GGGB,GGBG,GBGG,BGGG}.

If there are two girls and two boy then there are six possibilities, that is, {GGBB,GBBG,BBGG,BGBG,GBGB,BGGB}.

If there are three boys and one girl then there are four possibilities, that is, {GBBB,BGBB,BBGB,BBBG}.

If there is no girl then there is only one possibility, that is, {BBBB}.

So, the sample space is the collection of all these possibilities

To determine

(b)

To find:

The probability that the couple will have only boys.

To determine

(c)

To find:

The probability that the couple will have two boys and two girls.

To determine

(d)

To find:

The probability that the couple will have four children of the same gender.

To determine

(e)

To find:

The probability that the couple will have at least two girls.

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