Explanation Given information: A family is randomly selected that has two children. Having a boy or a girl are equally likely events. Concept used: The conditional probability P ( E | F ) of E if event F occurs can be expressed as, P ( E | F ) = n ( E ∩ F ) n ( F ) ....... (1) Here, E and F are the event in sample space. The number of element in event F is n ( F ) and the number of common element in event E and event F is n ( E ∩ F ) . Calculation: The sample space is the collection of all possible outcomes of an experiment. The sample space of having two children in a family is, S = { B G , G B , G G , B B } Consider n ( S ) as the number of element in sample space S . The number of element in sample space S can be calculated as, n ( S ) = 4 Consider A as the event that oldest child is a boy. The favorable outcomes of event A is, A = { B B , B G } Consider C as the event that both children are the boys, n ( C ) as the number of element in event C and P ( C ) as the probability of event C To determine (b) To find: The probability of event that the family has two boys if one child is a boy occur.

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

7th Edition

ISBN: 9781305718944

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

Videos

Question

Chapter 9.2, Problem 68E

To determine

(a)

To find:

The probability of event that the family has two boys if the oldest child is a boy.

To determine

(b)

To find:

The probability of event that the family has two boys if one child is a boy occur.

Expert Solution & Answer

Chapter 9 Solutions

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

Ch. 9.1 - The Fundamental Counting Principle says that if...Ch. 9.1 - The number of ways of arranging r objects form n...Ch. 9.1 - The number of ways of choosing r objects from n...Ch. 9.1 - True or False? In counting combinations, order...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

(a) To find: The probability of event that the family has two boys if the oldest child is a boy.

Solution Summary: The author calculates the probability of event that the family has two boys if the oldest child is a boy. The sample space is the collection of all possible outcomes of an experiment.