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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

Family Planning A couple intends to have two children. What is the probability that they will have one child of each sex? The French mathematician D’Alembert analyzed this problem (incorrectly) by reasoning that three outcomes are possible: two boys, or two girls, or one child of each sex. He concluded that the probability of having one of each sex is 1 3 , mistakenly that the three outcomes are equally likely.

(a) Model this problem with a pair of coins (using “heads” for boys and “tails” for girls), or write a program to model the problem. Perform the experiment 40 or more times, counting the number of boy-girl combinations. Estimate the probability of having one child of each sex.

(b) Calculate the correct probability of having one child of each sex, and compare this with your result from part (a).

To determine

(a)

To perform:

The experiment 40 or more times and estimate the probability of having one child of each sex.

Explanation

Given:

A couple intends to have two children. The French mathematician D’Alembert analyzed this problem (incorrectly) by reasoning that three outcomes are possible: two boys, or two girls, or one child of each sex. He concluded that the probability of having one of each sex is 13, mistakenly that the three outcomes are equally likely.

Approach:

The probability of an event E is,

P(E)=n(E)n(S)(1).

Here, n(E) denotes the favorable outcome, n(S) denotes the total outcome.

Calculation:

When two coins are flipped together the possible outcomes are 4.

This implies the outcomes are {HH,HT,TH,TT}

To determine

(b)

To find:

The probability of having one child of each sex.

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Chapter 14 Solutions

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