Question 1

A tire manufacturer advertises, "the median life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?
A) 1/10 or 0.10
B) ¼ or 0.25
C) 1/64 or 0.0156
D) 1/16 or 0.0625

Accepted Answer

The answer of A tire manufacturer advertises, "the median life...

Question 2

How many permutations of the two letters C and D are possible?
A) 1
B) 0
C) 2
D) 8

Accepted Answer

There are two letters, C and D, and two possible arrangements: CD and DC. Therefore, there are only two possible permutations.

Question 3

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
A) 0.20
B) 0.08
C) 0.25
D) 0.80

Accepted Answer

The total percentage of females who did not attend college is 20% (100% - 80% females who attended college). Therefore, the probability of selecting a female who did not attend college is 0.20.

Question 4

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A) 0.20
B) 0.08
C) 0.25
D) 0.72

Accepted Answer

80% of the trainees are female, so the probability of selecting a female is 0.8. Of these females, 90% attended college, so the probability of a female trainee attending college is 0.8 x 0.9 = 0.72. Therefore, the answer is D.

Question 5

A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek and 40% read U.S. News & World Report. Ten percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
A) 0.85
B) 0.06
C) 1.00
D) 0.65

Accepted Answer

We can use the formula: 
P(Time or US News) = P(Time) + P(US News) - P(Time and US News)

Plugging in the given values, we get: 
P(Time or US News) = 0.35 + 0.40 - 0.10 = 0.65

Therefore, the probability that a particular top executive reads either Time or U.S. News & World Report regularly is 0.65, which corresponds to option (D).

Question 6

A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?
A) 1/120 or 0.00083
B) 1/16 or 0.0625
C) ⅛ or 0.125
D) 1/495 or 0.002

Accepted Answer

The total number of ways to form a 4-member search committee from a board of 12 directors is:
12C4 = (12!)/(4!8!) = 495
The number of ways to form a search committee with four women is:
4C4 * 8C0 = 1 * 1 = 1
(Choosing all four women from the four available, and no men from the eight available)
So the probability of selecting a search committee with all four women is:
1/495

Question 7

What does  equal?
A) 640
B) 36
C) 10
D) 120

Accepted Answer

The answer of What does  equal?
A) 640
B) 36
C) 10
D)...

Question 8

There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?
A) ½ or 0.50
B) ¼ or 0.25
C) 1/120 or about 0.0083
D) 1/15 or about 0.07

Accepted Answer

The probability of selecting the first defective roll is 3/10. After removing one defective roll, there are 2 defective rolls left out of 9 total rolls. The probability of selecting a second defective roll is 2/9. Multiply these probabilities: (3/10) * (2/9) = 1/15.

Question 9

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did attend college?
A) P (female) P(did not attend college | female)
B) P (did attend college) P (female | did not attend college)
C) P (female) P(did attend college | female)
D) P (did attend college)

Accepted Answer

We want to find the probability of selecting a female who did attend college. Using Bayes' theorem, we can write:
P(female and did attend college) = P(female) * P(did attend college | female)
We are given that 80% of the trainees are female, so P(female) = 0.8. We are also given that 90% of the females attended college, so P(did attend college | female) = 0.9. Therefore,
P(female and did attend college) = 0.8 * 0.9 = 0.72
Thus, the probability of selecting a female who did attend college is 0.72.

Question 10

Giorgio offers the person who purchases an 8 ounce bottle of Allure two free gifts, either an umbrella, a 1 ounce bottle of Midnight, a feminine shaving kit, a raincoat or a pair of rain boots. If you purchased Allure what is the probability you randomly selected an umbrella and a shaving kit in that order?
A) 0.00
B) 1.00
C) 0.05
D) 0.20

Accepted Answer

The probability of selecting an umbrella first is 1/5, and the probability of then selecting a shaving kit is 1/4 (since one gift has already been selected). Therefore, the probability of selecting an umbrella and then a shaving kit is (1/5) x (1/4) = 0.05 or 5%.

Question 11

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the four types of components are sold together, they form a "system." How many different systems can the electronics firm offer?
A) 36
B) 18
C) 72
D) 144

Accepted Answer

The electronics firm has 4 choices for stereo receivers, 3 choices for CD decks, and 6 choices for speaker brands. Using the multiplication principle, the total number of possible systems is: 4 x 3 x 6 = 72. Therefore, the correct answer is option C.

Question 12

A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each, purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?
A) 0.50
B) 0.062
C) 0.33
D) 0.75

Accepted Answer

The probability of Sue getting a red gumball is 100/400 = 0.25. 
Assuming she gets a red gumball, there would be 99 red gumballs left out of 399. 
The probability of Jim getting a red gumball, given that Sue already got one, is 99/399 = 0.248. 
The probability of both events happening is the product of each individual probability: 
0.25 x 0.248 = 0.062. 
Therefore, the likelihood of both Sue and Jim getting red gumballs is 0.062 or approximately 6.2%. Thus, the best choice is B.

Question 13

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A) P (male) P (did not attend college | male)
B) P (did not attend college) P (male | did not attend college)
C) P (male) P (did not attend college)
D) P (did not attend college)

Accepted Answer

P (male) P (did not attend college | male) = 0.20 * (1 - 0.78) = 0.044

Question 14

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?
A) 4
B) 24
C) 120
D) 37

Accepted Answer

Since the order in which the sales representative calls on the hospitals does not matter, we are looking for the number of combinations, not permutations. The formula for combinations is n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose. Here, n = 4 (the hospitals) and r = 4 (since he has to call all of them), so the calculation is 4! / (4!(4-4)!) = 4! / (4!0!) = 1. However, considering the context, the correct interpretation should be the number of permutations since the question might imply the sequence of visits matters (immaterial in the question context seems to imply the sequence can be any), which is 4! = 24.

Question 15

A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?
A) 5
B) 10
C) 15
D) 20

Accepted Answer

There are 5 possible base choices and 4 possible shade choices. To determine the total number of arrangements, we can use the fundamental counting principle and multiply the number of choices:

5 base choices x 4 shade choices = 20

Therefore, there are 20 different arrangements of base and shade that can be offered. Choice D is the correct answer.

Question 16

The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
A) 5,040
B) 620
C) 10,200
D) 120

Accepted Answer

The number of different code groups can be calculated by finding the number of permutations of 4 digits chosen from 10, which is 10P4 = 10! / (10-4)! = 10 × 9 × 8 × 7 = 5,040.

Question 17

A firm offers routine physical examinations as part of a health service program for its employees. The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
A) 0.20
B) 0.25
C) 0.50
D) 1.00

Accepted Answer

The answer of A firm offers routine physical examinations as...

Question 18

A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?
A) 0.95
B) 0.35
C) 0.55
D) 0.05

Accepted Answer

The probability of visiting at least one attraction can be found by adding the probability of visiting just Yellowstone (50% - 35% = 15%), just Grand Tetons (40% - 35% = 5%) and visiting both (35%). So, the probability is 15% + 5% + 35% = 55%, which is option C.

Question 19

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?
A) 3/20 or 0.15
B) 3/17 or 0.176
C) ¼ or 0.25
D) 3/190 or 0.01579

Accepted Answer

There are a total of 20 electric toothbrushes, and 3 of them are defective. Therefore, the probability that the first toothbrush sold is defective is 3/20. After one defective toothbrush has been sold, there are 2 defective toothbrushes left out of 19 toothbrushes. Therefore, the probability that the second toothbrush sold is also defective is 2/19. 
The probability that both events occur together (that the first two toothbrushes sold are defective) is the product of their probabilities, which is:
P(both defective) = (3/20) x (2/19) = 3/190, which is approximately 0.01579. 
Therefore, the answer is choice D.

Question 20

In a management trainee program, 80 percent of the trainees are female, 20 percent male. Ninety percent of the females attended college, 78 percent of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a male who did NOT attend college?
A) 0.044
B) 0.440
C) 0.256
D) 0.801

Accepted Answer

Out of all trainees, 20% are male. Out of all male trainees, 78% attended college, so 22% did not attend college. Therefore, the probability of selecting a male who did not attend college is:
0.20 x 0.22 = 0.044

Quiz 5: A Survey of Probability Concepts

How many permutations of the two letters C and D are possible?

A board of directors consists of eight men and four women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women?

What does equal?

There are 10 rolls of film in a box and 3 are defective. Two rolls are selected without replacement. What is the probability of selecting a defective roll followed by another defective roll?

An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the four types of components are sold together, they form a "system." How many different systems can the electronics firm offer?

A gumball machine has just been filled with 50 black, 150 white, 100 red and 100 yellow gum balls that have been thoroughly mixed. Sue and Jim, each, purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?

A lamp manufacturer has developed five lamp bases and four lampshades that could be used together. How many different arrangements of base and shade can be offered?

A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Grand Tetons and 35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?

Three defective electric toothbrushes were accidentally shipped to a drugstore by the manufacturer along with 17 non-defective ones. What is the probability that the first two electric toothbrushes sold will be returned to the drugstore because they are defective?