Skip to main content
Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 4 - ProbabilityProblem 4.3.7b
Chapter 4, Problem 4.3.7b

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.


b. The probability that all three children are boys.

Verified step by step guidance
1
Step 1: Understand the problem. We are tasked with finding the probability that all three children in a family are boys, given that the probability of a single child being a boy is 0.512.
Step 2: Recall the multiplication rule for independent events. Since the gender of each child is independent of the others, the probability of all three children being boys is the product of the probabilities of each child being a boy.
Step 3: Write the formula for the probability of all three children being boys: \( P(\text{all boys}) = P(\text{boy}) \times P(\text{boy}) \times P(\text{boy}) \).
Step 4: Substitute the given probability of a single child being a boy (0.512) into the formula: \( P(\text{all boys}) = 0.512 \times 0.512 \times 0.512 \).
Step 5: Multiply the probabilities together to find the final result. This will give you the probability that all three children are boys.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, the probability of a baby being a boy is given as 0.512, indicating that there is a 51.2% chance of a boy being born. Understanding probability is essential for calculating the chances of multiple independent events occurring together.
Recommended video:
5:37
Introduction to Probability

Independent Events

Independent events are those whose outcomes do not affect each other. In the case of having three children, the gender of each child is independent of the others. This means that the probability of each child being a boy remains constant at 0.512, regardless of the genders of the other children.
Recommended video:
05:54
Probability of Multiple Independent Events

Multiplication Rule of Probability

The multiplication rule of probability states that the probability of multiple independent events occurring together is the product of their individual probabilities. For this question, to find the probability that all three children are boys, you would multiply the probability of having a boy (0.512) by itself three times, reflecting the independence of each child's gender.
Recommended video:
05:54
Probability of Multiple Independent Events
Related Practice
Textbook Question

In Exercises 21-28, find the probability and answer the questions.


Genetics: Eye Color Each of two parents has the genotype brown/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is more complicated than that.)


b. What is the probability that a child of these parents will have the blue/blue genotype?

155
views
Textbook Question

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a \$1 bill, some college students were given four quarters and others were given a \$1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).



Denomination Effect


b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.


128
views
Textbook Question

Births in Vietnam In Vietnam, the probability of a baby being a boy is 0.526 (based on the data available at this writing). For a family having four children, find the following.


b. The probability that all four children are girls.


166
views
Textbook Question

In Exercises 21-28, find the probability and answer the questions.


Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.


b. Would it be unlikely for him to guess correctly on his first try?

261
views
Textbook Question

Corporate Officers and Committees The Self Driving Unicycle Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO), and chief human resources officer (CHR). It must also appoint a strategic planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee.


b. How many different ways can a committee of five be appointed?


146
views
Textbook Question

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)



Testing for Marijuana Use


b. How many of the subjects had a true negative result?

132
views