×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

Betting on Sports According to a Gallup Poll, about 17% of

Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III ISBN: 9780321757272 73

Solution for problem 32E Chapter 5.3

Statistics: Informed Decisions Using Data | 4th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III

Statistics: Informed Decisions Using Data | 4th Edition

4 5 0 296 Reviews
12
2
Problem 32E

 Problem 32E

Betting on Sports According to a Gallup Poll, about 17% of adult Americans bet on professional sports. Census data indicate that 48.4% of the adult population in the United States is male.

(a) Assuming that betting is independent of gender, compute the probability that an American adult selected at random is a male and bets on professional sports.

(b) Using the result in part (a), compute the probability that an American adult selected at random is male or bets on professional sports.

(c) The Gallup poll data indicated that 10.6% of adults in the United States are males and bet on professional sports. What does this indicate about the assumption in part (a)?

(d) How will the information in part (c) affect the probability you computed in part (b)?

Step-by-Step Solution:

Step 1 of 3:

About 17% of adult Americans bet on professional sports.

Census data indicate that 48.4% of the adult population in the United States is male.

We have to find the following.

The probability that an American adult selected at random is male and bets on professional sports, by assuming that betting is independent of gender.The probability that an American adult selected at random is male or bets on professional sports by using part (a).The poll data indicated that 10.6% of adults in the United States are males and bet on professional sports, we have to describe what does this indicate about the assumption in part (a).We have to describe how will the information in part (c) affect the probability that computed in part (b).

Step 2 of 3:

Let us define the events:

A: {Americans bet on professional sports}

B: {Adult population in the United States is male}

From the given information:

                                                              P (A) = 0.17

                                                              P (B) = 0.484

(a)

Here betting is independent of gender.

Two events are said to be independent if P (AB) = P (A)P (B).

P (The selected adult is a male and bets on professional sports) = P (AB)

                                                                                                     = P (A)P (B)

                                                                                                     = 0.17 0.484

                                                                                                     = 0.082

Therefore, the probability that an American adult selected at random is male and bets on professional sports, by assuming that betting is independent of gender is 0.082.

(b)

By the addition rule of probability:

                                                      P (AB) = P (A)+P (B)-P (AB)

P (The selected adult is a male or bets on professional sports) = P(AB)

                                                                                                    = P (A)+P (B)-P(A)

                                                                                                                                   [ from part (a)]

                                                                                                    = 0.17+0.484-(0.082)

                                                                                                    = 0.572

Therefore, the probability that an American adult selected at random is male or bets on professional sports is 0.572.

 

Step 3 of 3

Chapter 5.3, Problem 32E is Solved
Textbook: Statistics: Informed Decisions Using Data
Edition: 4
Author: Michael Sullivan, III
ISBN: 9780321757272

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Betting on Sports According to a Gallup Poll, about 17% of

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password