/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 The probability that a randomly ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 65

The probability that a randomly selected college student attended at least one major league baseball game last year is .12. What is the complementary event? What is the probability of this complementary event?

Short Answer

Expert verified
The complementary event is that a randomly selected college student did not attend any major league baseball game last year. The probability of this complementary event is 0.88.

Step by step solution

01

Understand the Concept of Complementary Events

In probability theory, for any event A, the complementary event \( A' \) is the event that A does not occur. Here, the event A is a college student attending at least one major league baseball game last year.
02

Identify the Complementary Event

Here, the complementary event \( A' \) would be the event that a randomly selected college student did not attend any major league baseball game last year.
03

Calculate the Probability of the Complementary Event

In probability, the sum of the probabilities of an event and its complementary event always equals 1. The probability of the complementary event can be calculated by subtracting the probability of the event from 1. So, the probability of \( A' \) is \( 1 - 0.12 = 0.88 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses. $$\begin{array}{lccc} \hline & \text { In Favor } & \text { Against } & \text { No Opinion } \\ \hline \text { Male } & 395 & 405 & 100 \\ \text { Female } & 300 & 680 & 120 \\ \hline \end{array}$$ a. If one person is selected at random from these 2000 adults, find the probability that this person is i. in favor of cloning ii. against cloning iii. in favor of cloning given the person is a female iv. a male given the person has no opinion b. Are the events "male" and "in favor" mutually exclusive? What about the events "in favor" and "against?" Why or why not? c. Are the events "female" and "no opinion" independent? Why or why not?

A random sample of 400 college students was asked if college athletes should be paid. The following table gives a two-way classification of the responses. $$\begin{array}{lcc} \hline & \text { Should Be Paid } & \text { Should Not Be Paid } \\ \hline \text { Student athlete } & 90 & 10 \\ \text { Student nonathlete } & 210 & 90 \end{array}$$ a. If one student is randomly selected from these 400 students, find the probability that this student i. is in favor of paying college athletes ii. favors paying college athletes given that the student selected is a nonathlete iii. is an athlete and favors paying student athletes iv. is a nonathlete or is against paying student athletes b. Are the events "student athlete" and "should be paid" independent? Are they mutually exclusive? Explain why or why not.

Five hundred employees were selected from a city's large private companies and asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way classification table was prepared. $$\begin{array}{llc} \hline & \text { Yes } & \text { No } \\ \hline \text { Men } & 225 & 75 \\ \text { Women } & 150 & 50 \\ \hline \end{array}$$ a. Suppose one employee is selected at random from these 500 employees. Find the following probabilities. i. Probability of the intersection of events "woman" and "yes" ii. Probability of the intersection of events "no" and "man" b. Mention what other joint probabilities you can calculate for this table and then find them. You may draw a tree diagram to find these probabilities.

Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two- way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as. or worse off than their parents. $$\begin{array}{lccc} \hline & \begin{array}{c} \text { Less Than } \\ \text { High School } \end{array} & \begin{array}{c} \text { High } \\ \text { School } \end{array} & \begin{array}{c} \text { More Than } \\ \text { High School } \end{array} \\ \hline \text { Better off } & 140 & 450 & 420 \\ \text { Same as } & 60 & 250 & 110 \\ \text { Worse off } & 200 & 300 & 70 \\ \hline \end{array}$$ a. Suppose one adult is selected at random from these 2000 adults. Find the following probabilities. i. \(P\) (better off and high school) ii. \(P(\) more than high school and worse off ) b. Find the joint probability of the events "worse off" and "better off." Is this probability zero? Explain why or why not.

A trimotor plane has three engines-a central engine and an engine on each wing. The plane will crash only if the central engine fails and at least one of the two wing engines fails. The probability of failure during any given flight is \(.005\) for the central engine and \(.008\) for each of the wing engines. Assuming that the three engines operate independently, what is the probability that the plane will crash during a flight?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.