Explanation Given: The number of envelopes is 6. Four envelopes are empty and two envelopes contain a $ 100 bill. Explanation: Consider the experiment of choosing 2 envelopes from 6 envelopes. Four envelopes are empty and two envelopes contain a $100 bill. Assume that, E represents the event that at least one $100 bill is chosen and F represents the event that no $100 bill is chosen at all. The number of elements in the sample space will be equal to the number of ways of selecting 2 envelopes from 6 envelopes. That is, n ( S ) = C ( 6 , 2 ) = 6 ! 2 ! × ( 6 − 2 ) ! = 6 × 5 × 4 ! 2 × 1 × 4 ! = 15 The event E will consist of choosing one $100 bill and two $100 bills. The number of ways of selecting 2 envelopes such that one envelope is from four empty envelopes and one envelope contains $100 bill is, C ( 2 , 1 ) × C ( 4 , 1 ) = 2 ! 1 ! × ( 2 − 1 ) ! × 4 ! 1 ! × ( 4 − 1 ) ! = 2 × 1 1 × 1 × 4 × 3 ! 1 × 3 ! = 2 × 4 = 8 The number of ways of selecting 2 envelopes such that both envelope contains $100 bill is, C ( 2 , 2 ) × C ( 4 , 0 ) = 2 ! 2 ! × ( 2 − 2 ) ! × 4 ! 0 ! × ( 4 − 0 ) ! = 2 ! 2 ! × 1 × 4 ! 1 × 4 ! = 1 × 1 = 1 So, the number of elements in the event E is, n ( E ) = 8 + 1 = 9 The event F will consist of choosing no $100 bill

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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 8.3, Problem 35E

To determine

The event that is more likely, to get at least one $100 bill or to get no $100 bill at all when two envelopes are chosen at random from 6 envelopes.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 34E

Chapter 8.3, Problem 36E

Students have asked these similar questions

A poll before the elections showed that in a given sample 79% of people vote for candidate C. How many people should be interviewed so that the pollsters can be 99% sure that from 75% to 83% of the population will vote for candidate C? Round your answer to the whole number.

Suppose a random sample of 459 married couples found that 307 had two or more personality preferences in common. In another random sample of 471 married couples, it was found that only 31 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common. Find a95% confidence interval for . Round your answer to three decimal places.

A history teacher interviewed a random sample of 80 students about their preferences in learning activities outside of school and whether they are considering watching a historical movie at the cinema. 69 answered that they would like to go to the cinema. Let p represent the proportion of students who want to watch a historical movie. Determine the maximal margin of error. Use α = 0.05. Round your answer to three decimal places.

Chapter 8 Solutions

Finite Mathematics (11th Edition)

Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - In Exercises 112, evaluate the factorial or...Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - In Exercises 1-12, evaluate the factorial or...

Knowledge Booster

Learn more about

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

The event that is more likely, to get at least one $100 bill or to get no $100 bill at all when two envelopes are chosen at random from 6 envelopes.

Solution Summary: The author explains that the number of envelopes in the sample space is equal to how many ways one envelope is selected from a 6 envelope.

Concept explainers

Videos

The event that is more likely, to get at least one $100 bill or to get no $100 bill at all when two envelopes are chosen at random from 6 envelopes.

Want to see the full answer?

Chapter 8 Solutions