Question 1

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

Accepted Answer

No, gender is not independent of type of job.
Select a category of gender (male) and a category of job status (faculty), if the two are independent of each other, then:
P(M) = P(M | FA)
Since P(M) == 0.667
and P(M | FA) == 0.9167
0.667 ≠ 0.9167

Question 2

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table.  What is the probability that Cheryl packed a given dinner and forgot to include a napkin?

Accepted Answer

P(Cheryl ∩ Forgot napkin) = (.20)(.10) = 0.02

Question 3

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table.  What is the probability that there is not a napkin included for a given order?

Accepted Answer

P(No Napkin) = (.25)(.06) + (.20)(.02) + (0.20)(.10) + (.35)(.04) = .053

Question 4

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that none will graduate?

Accepted Answer

(.15)(.15)(.15) = .003375

Question 5

It is very common for a television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that none of the three households viewed this special show?

Accepted Answer

(.618)(.618)(.618) = .236

Question 6

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that exactly one of the three graduates?

Accepted Answer

(.85)(.15)(.15) + (.15)(.85)(.15) + (.15)(.15)(.85) = .057375

Question 7

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at University A and rejected at University B?

Accepted Answer

(.25)(.60) = 0.15

Question 8

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at both universities?

Accepted Answer

(.25)(.40) = 0.10

Question 9

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is either a woman or a Democrat.

Accepted Answer

P(W ∪ D) = P(W) + P(D) - P(W ∩ D)
= (40/80) + (65/80) - (35/80) = .877

Question 10

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will not be accepted at either university?

Accepted Answer

(.75)(.60) = 0.45

Question 11

It is very common for a television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that exactly one of the three households viewed the special show?

Accepted Answer

(.382)(.618)(.618) + (.618)(.382)(.618) + (.618)(.618)(.382) = .4376

Question 12

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table.  You just purchased a dinner and found that there is no napkin in your bag. What is the probability that Jan prepared your order?

Accepted Answer

P(Jan | No napkin) === .0755

Question 13

It is very common for a television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that all three households viewed this special show?

Accepted Answer

(.382)(.382)(.382) = .05574

Question 14

Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Also recorded was the proportion of all dinners packed by each employee. Related information is given in the table.  You just purchased a dinner and found that there is no napkin in your bag. What is the probability that Cheryl prepared your order?

Accepted Answer

P(Cheryl | No napkin) === .37774

Question 15

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a Democrat or a Republican.

Accepted Answer

All voters in the survey were either D or R. Therefore, the probability is 1.

Question 16

A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that all graduate?

Accepted Answer

(.85)(.85)(.85) = 0.614

Question 17

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a male Republican.

Accepted Answer

(10/80) = .125

Question 18

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at one, and only one, university?

Accepted Answer

(.25)(.60) + (.75)(.40) = 0.45

Question 19

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. Of the applicants with similar qualities, only 10 percent are accepted into both University A and University B. Is the acceptance decision at University A independent of the acceptance decision at University B?

Accepted Answer

Yes, the two decisions are statistically independent. If the MBA acceptance decisions are independent at the two universities, then
P(Accepted at A) = P(Accepted at A given Rejected at B).
P(Accepted at A) = .25 = P(Accept at A | Reject at B)
=== .25

Question 20

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted by at least one of the two universities?

Accepted Answer

1 − (.75)(.60) = 0.55

Quiz 4: Probability and Probability Models

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