Question 1

A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel?

Accepted Answer

AEIOU; 5 vowels out of 26 letters.

Question 2

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is a member of the faculty?

Accepted Answer

P(FA) == .40

Question 3

At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table.  If a student has received a grade of C, what is the probability that the student is female?

Accepted Answer

P(female | C) == .90

Question 4

If events A and B are mutually exclusive, calculate P(A|B).

Accepted Answer

Mutually exclusive events have intersection = 0. Therefore, the conditional probability is also 0.

Question 5

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is female or works as an hourly staff member?

Accepted Answer

P(F ∪ HA) =+-= 0.533

Question 6

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is female or works as a member of the faculty?

Accepted Answer

P(F ∪ FA) =+-= 0.70

Question 7

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither buys beer nor buys cigars.

Accepted Answer

11ead627_0aae_12a8_93a1_8d053add9586_TB7056_00

Question 8

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys beer.

Accepted Answer

11ead627_0aad_eb97_93a1_773637f28d8a_TB7056_00 P(Beer) === .04

Question 9

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table.  If a student has received a grade of C, what is the probability that the student is male?

Accepted Answer

P(Male | C) == .10

Question 10

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is female, given that the employee is a salaried member of the staff?

Accepted Answer

P(F | SS) === 0.625

Question 11

If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B.

Accepted Answer

(.2)(.8) = .16

Question 12

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is male and salaried staff?

Accepted Answer

P(M and SS) == 0.10

Question 13

If a product is made using five individual components, and P(product meets specifications) = P(E) = .98, what is the probability of an individual component meeting specifications, assuming that this probability is the same for all five components?

Accepted Answer

= .996

Question 14

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is male?

Accepted Answer

P(M) == .667

Question 15

An urn contains five white, three red, and four black balls. Three are drawn at random and not placed back into the urn. What is the probability that no ball is red?

Accepted Answer

= .3818

Question 16

Employees of a local university have been classified according to gender and job type.  Are gender and type of job mutually exclusive?

Accepted Answer

No, gender and job type are not mutually exclusive.
P(M) == .667
P(FA) == 0.40
P(M ∩ FA) =≠ 0

Question 17

The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring?

Accepted Answer

P(B) = P(A ∩ B) / P(A | B) = .5/.61 = 0.81967

Question 18

Employees of a local university have been classified according to gender and job type.  If an employee is selected at random, what is the probability that the employee is a member of the hourly staff, given that the employee is female?

Accepted Answer

P(HS | F) === 0.400

Question 19

What is the probability of rolling a six with a fair die five times in a row?

Accepted Answer

(1/6)⁵ = 1/7,776

Question 20

What is the probability that any two people chosen at random were born on the same day of the week?

Accepted Answer

Set up sample space: 7² = 49; same day: 7 sample space outcomes.

Quiz 4: Probability and Probability Models

A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the faculty?

At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student has received a grade of C, what is the probability that the student is female?

If events A and B are mutually exclusive, calculate P(A|B) .

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female or works as an hourly staff member?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female or works as a member of the faculty?

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither buys beer nor buys cigars.

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys beer.

At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student has received a grade of C, what is the probability that the student is male?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female, given that the employee is a salaried member of the staff?

If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B.

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male and salaried staff?

If a product is made using five individual components, and P(product meets specifications) = P(E) = .98, what is the probability of an individual component meeting specifications, assuming that this probability is the same for all five components?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male?

An urn contains five white, three red, and four black balls. Three are drawn at random and not placed back into the urn. What is the probability that no ball is red?

Employees of a local university have been classified according to gender and job type. Are gender and type of job mutually exclusive?

The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the hourly staff, given that the employee is female?

What is the probability of rolling a six with a fair die five times in a row?

What is the probability that any two people chosen at random were born on the same day of the week?