Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
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Chapter 4.3, Problem 17E

(a)

To determine

To find:

The probability that Mrs. Harvey selects a male, given that she chooses from only the sophomores.

(a)

Expert Solution
Check Mark

Answer to Problem 17E

Solution:

The required probability is 0.444.

Explanation of Solution

Given information:

Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.

Mrs. Harvey’s Algebra Class
Male Female
Freshman 9 13
Sophomore 4 5
Junior 4 2
Senior 2 3

Definition:

Dependent Event:

Two events are dependent if one event happening effect the probability of the other event happening.

Formula used:

If EandF are two dependent events, then the formula to calculate the probability that F occurs given that E occurs, is,

P(F/E)=P(EandF)P(E)

Calculation:

Total number of student is 42.

There are 4 male and 5 female sophomores.

Total number of sophomore is 9.

Let A be the event of choosing a male and B be the event of choosing a sophomore.

Calculate the probability of event AandB.

P(AandB)=442

Calculate the probability of event B.

P(B)=942

Use the formula to calculate the conditional probability of event A, when another event B has already occurred.

P(A/B)=P(AandB)P(B)=442942=49=0.444

Conclusion:

Thus, the probability that Mrs. Harvey selects a male, given that she chooses from only the sophomores is 0.444.

(b)

To determine

To find:

The probability that Mrs. Harvey selects a junior, given that she chooses a female.

(b)

Expert Solution
Check Mark

Answer to Problem 17E

Solution:

The required probability is 0.0870.

Explanation of Solution

Given information:

Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.

Mrs. Harvey’s Algebra Class
Male Female
Freshman 9 13
Sophomore 4 5
Junior 4 2
Senior 2 3

Definition:

Dependent Event:

Two events are dependent if one event happening effect the probability of the other event happening.

Formula used:

If EandF are two dependent events, then the formula to calculate the probability that F occurs given that E occurs, is,

P(F/E)=P(EandF)P(E)

Calculation:

Total number of student is 42.

There are 4 male and 2 female junior.

Total number of junior is 6.

Total number of female is (13+5+2+3)=23.

Let A be the event of choosing a junior and B be the event of choosing a female.

Calculate the probability of event AandB.

P(AandB)=642

Calculate the probability of event B.

P(B)=2342

Use the formula to calculate the conditional probability of event A, when another event B has already occurred.

P(A/B)=P(AandB)P(B)=6422342=623=0.0870

Conclusion:

Thus, the probability that Mrs. Harvey selects a junior, given that she chooses a female is 0.0870.

(c)

To determine

To find:

The probability that Mrs. Harvey selects a female, given that she chooses a junior.

(c)

Expert Solution
Check Mark

Answer to Problem 17E

Solution:

The required probability is 0.333.

Explanation of Solution

Given information:

Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.

Mrs. Harvey’s Algebra Class
Male Female
Freshman 9 13
Sophomore 4 5
Junior 4 2
Senior 2 3

Definition:

Dependent Event:

Two events are dependent if one event happening effect the probability of the other event happening.

Formula used:

If EandF are two dependent events, then the formula to calculate the probability that F occurs given that E occurs, is,

P(F/E)=P(EandF)P(E)

Calculation:

Total number of student is 42.

There are 4 male and 2 female junior.

Total number of junior is 6.

Total number of female is (13+5+2+3)=23.

Let A be the event of choosing a female and B be the event of choosing a junior.

Calculate the probability of event AandB.

P(AandB)=242

Calculate the probability of event B.

P(B)=642

Use the formula to calculate the conditional probability of event A, when another event B has already occurred.

P(A/B)=P(AandB)P(B)=242642=26=0.333

Conclusion:

Thus, the probability that Mrs. Harvey selects a female, given that she chooses a junior is 0.333.

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Chapter 4 Solutions

Beginning Statistics, 2nd Edition

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.CR - Prob. 1CRCh. 4.CR - Prob. 2CRCh. 4.CR - Prob. 3CRCh. 4.CR - Prob. 4CRCh. 4.CR - Prob. 5CRCh. 4.CR - Prob. 6CRCh. 4.CR - Prob. 7CRCh. 4.CR - Prob. 8CRCh. 4.CR - Prob. 9CRCh. 4.CR - Prob. 10CRCh. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Prob. 17CRCh. 4.CR - Prob. 18CRCh. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Prob. 23CRCh. 4.CR - Prob. 24CRCh. 4.CR - Prob. 25CR
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