Question 1

How many permutations of the three letters C,D,and E are possible?
A)3
B)0
C)6
D)8

Accepted Answer

There are 3 options for the first letter, 2 options left for the second letter, and only 1 option left for the third letter. So, the total number of permutations is 3x2x1=6.

Question 2

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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

The correct formula to use is P(male) * P(did not attend college | male) because we are looking for the probability of being a male and then, given that condition, not having attended college.

Question 3

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 probability of needing corrective shoes is 0.08, the probability of needing major dental work is 0.15, and the probability of needing both is 0.03. So the probability of needing either is 0.08 + 0.15 - 0.03 = 0.20.

Question 4

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. A total of 10% 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

To find the probability that a particular top executive reads either Time or U.S. News & World Report regularly, we need to add the probabilities of reading Time or U.S. News & World Report, and subtract the probability of reading both magazines (to avoid double-counting).

P(Time or U.S. News) = P(Time) + P(U.S. News) - P(Time and U.S. News)

P(Time or U.S. News) = 0.35 + 0.40 - 0.10

P(Time or U.S. News) = 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 choice D.

Question 5

An electronics firm sells four models of stereo receivers,three amplifiers,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 number of different systems that can be offered can be found by multiplying the number of options for each component. So, the total number of systems would be 4 x 3 x 6 = 72. Therefore, the correct answer is C.

Question 6

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

To find the probability that a vacationer will visit at least one of these attractions, we need to add the probabilities of visiting Yellowstone, Grand Tetons, or both. However, we need to subtract the probability of visiting both since we don't want to count those vacationers twice.

P(Yellowstone or Grand Tetons) = P(Yellowstone) + P(Grand Tetons) - P(Both)

P(Yellowstone or Grand Tetons) = 0.50 + 0.40 - 0.35

P(Yellowstone or Grand Tetons) = 0.55

Therefore, the probability that a vacationer will visit at least one of these magnificent attractions is 0.55, which is option C.

Question 7

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-in other words,the same number cannot be used more than once in a total sequence. As examples,2,256,2,562,or 5,559 would not be permitted. How many different code groups can be designed?
A)5,040
B)620
C)10,200
D)120

Accepted Answer

Since repetitions are not allowed and each code group consists of 4 digits selected from 0-9 (10 options), the number of different code groups can be designed using the permutation formula for selecting 4 unique digits out of 10, which is 10P4 = 10! / (10-4)! = 10*9*8*7 = 5,040.

Question 8

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

Accepted Answer

To find the probability that the person selected is a female who attended college, we need to multiply the probability of selecting a female by the probability of a female attending college.
Probability of selecting a female = 0.80
Probability of a female attending college = 0.90
Therefore, the probability of selecting a female who attended college = 0.80 x 0.90 = 0.72. Thus, the answer is D.

Question 9

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

Accepted Answer

There is no clear indication or context provided to determine what the given sequence of characters represents, so no mathematical calculation or deduction can be made to arrive at a definitive answer. Therefore, the only reasonable option is to select the choice that acknowledges the lack of information and treats the question as unanswerable or irrelevant.

Question 10

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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

We know that 80% of the trainees are female, and 90% of females attended college, so the percentage of females who did not attend college is 10%. 
Therefore, the probability of selecting a female who did not attend college is (0.80)*(0.10) = 0.08. 
Hence, the answer is choice B.

Question 11

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)1/4 or 0.25
C)1/64 or 0.0156
D)1/16 or 0.0625

Accepted Answer

The median life of 50,000 miles means that 50% of the tires will last less than 50,000 miles. The probability that one tire wears out before 50,000 miles is 0.5. For all four tires to wear out before 50,000 miles, the probability is (0.5)^4 = 0.0625.

Question 12

There are 10 AAA batteries in a box and 3 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?
A)1/2 or 0.50
B)1/4 or 0.25
C)1/120 or about 0.0083
D)1/15 or about 0.07

Accepted Answer

The probability of selecting a defective battery first is 3/10. After removing one defective battery, there are now 9 batteries left, with 2 being defective. The probability of then selecting another defective battery is 2/9. Multiplying these probabilities gives (3/10) * (2/9) = 6/90 = 1/15.

Question 13

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended 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 attended college. Using the conditional probability formula, we have:

P(female and attended college) = P(attended college | female) * P(female)

From the given information, P(female) = 0.8 and P(attended college | female) = 0.9. Therefore,

P(female and attended college) = 0.9 * 0.8 = 0.72

So, the probability of selecting a female who attended college is 0.72, which is given by the expression P(female)P(attended college | female). Therefore, the correct choice is C. The other choices are incorrect because they do not take into account both the probability of being a female and the probability of attending college, or they use conditional probability incorrectly.

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 gumball machine has just been filled with 50 black,150 white,100 red,and 100 yellow gumballs that have been thoroughly mixed. Sue and Jim each purchase one gumball. What is the likelihood that both Sue and Jim will 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 or 1/4. After Sue takes one gumball, there will be 99 red gumballs left out of a total of 399. Therefore, the probability of Jim getting a red gumball after Sue takes one is 99/399. To find the probability of both events occurring, we multiply the probabilities: (1/4) x (99/399) = 99/15960, which simplifies to approximately 0.062 or 6.2%. Therefore, the correct answer is B.

Question 16

A lamp manufacturer designed 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

For each of the 5 lamp bases, there are 4 different lampshades that can be paired with it. Therefore, there are a total of 5 x 4 = 20 different arrangements of base and shade that can be offered. Therefore, the correct answer is D, 20.

Question 17

Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts,chosen from the following: 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 select an umbrella and a shaving kit in that order?
A)0.00
B)1.00
C)0.05
D)0.20

Accepted Answer

There are a total of 5 options to choose from. The probability of selecting an umbrella first is 1/5, then the probability of selecting a shaving kit next is 1/4 (since one item has already been selected). Therefore, the probability of selecting an umbrella and a shaving kit in that order is (1/5) x (1/4) = 0.05 or 5%. Therefore, the best choice would be C.

Question 18

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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

We use the formula for conditional probability:

P(Male AND Did Not Attend College) = P(Male) * P(Did Not Attend College | Male)

P(Male) = 0.20 (given)
P(Did Not Attend College | Male) = 1 - P(Attended College | Male) = 1 - 0.78 = 0.22

Therefore, P(Male AND Did Not Attend College) = 0.20 * 0.22 = 0.044

Question 19

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)1/8 or 0.125
D)1/495 or 0.002

Accepted Answer

The total number of ways to choose a 4-member search committee from twelve directors is:

12C4 = (12!)/(4!8!) = 495

The number of ways to choose all four women from the four available women is:

4C4 = 1

The number of ways to choose zero men from the eight available men is:

8C0 = 1

Thus, the probability of choosing all four women is:

(1)(1)/(495) = 1/495

Therefore, the best choice is D.

Question 20

A supplier delivers an order for 20 electric toothbrushes to a store. By accident,three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold are defective?
A)3/20 or 0.15
B)3/17 or 0.176
C)1/4 or 0.25
D)6/380 or 0.01579

Accepted Answer

The probability that the first electric toothbrush sold is defective is 3/20. 
After the first one is sold, there will be 19 toothbrushes left, including 2 defective ones. So, the probability that the second electric toothbrush sold is also defective is 2/19. 
The probability of both events happening together (the first two toothbrushes sold being defective) is the product of their probabilities: 
P(defective,defective) = (3/20) x (2/19) = 6/380 or 0.01579. 
Therefore, the correct answer is D.

Quiz 5: A Survey of Probability Concepts

How many permutations of the three letters C,D,and E are possible?

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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?

An electronics firm sells four models of stereo receivers,three amplifiers,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 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?

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?

What does equal?

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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?

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

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?

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

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

In a management trainee program,80% of the trainees are female,while 20% are male. Ninety percent of the females attended college; 78% 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 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 supplier delivers an order for 20 electric toothbrushes to a store. By accident,three of the electric toothbrushes are defective. What is the probability that the first two electric toothbrushes sold are defective?