Question 1

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)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

There are a total of 10 batteries, so the probability of selecting a defective battery on the first pick is 3/10. Since one battery has already been removed from the box, there are only 9 batteries remaining, and only 2 of them are defective. Therefore, the probability of selecting another defective battery on the second pick is 2/9. Since these events are dependent on each other (since we are selecting without replacement), we can multiply the probabilities to get the overall probability: (3/10) * (2/9) = 1/15 or approximately 0.07. Therefore, the best choice is D.

Question 2

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 attend college?
A)0.20
B)0.08
C)0.25
D)0.72

Accepted Answer

We can use the formula for conditional probability:
P(female and college) = P(female) * P(college | female)
P(female and college) = 0.8 * 0.9 = 0.72
Therefore, the probability that the person selected is a female who did attend college is 0.72.

Question 3

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, 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 that can be designed without repetition from 0 through 9 is calculated using permutations since the order of the numbers matters. There are 10 options for the first digit, 9 for the second (since one has been used), 8 for the third, and 7 for the fourth. Therefore, the total number of different code groups is 10 * 9 * 8 * 7 = 5,040.

Question 4

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 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 attended college, which can be expressed as P(female and did attend college) or P(did attend college | female). Using the formula for conditional probability, we have:

P(did attend college | female) = P(female and did attend college) / P(female)

We already know that P(female) = 0.8 and P(female and did attend college) = 0.8 x 0.9 = 0.72. Substituting these values, we get:

P(did attend college | female) = 0.72 / 0.8 = 0.9

Therefore, the probability that the selected person is a female who did attend college is 0.9 or 90%.

Question 5

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 base, there are four options of lampshades that could be used. Since there are five bases, the total number of arrangements is 5 x 4 = 20. Thus, the best choice is option D with the highest number of arrangements.

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 the two attractions, we need to add the probabilities of visiting Yellowstone Park and Grand Tetons and then subtract the probability of visiting both since we don't want to count these vacationers twice.

Probability of visiting Yellowstone Park = 50%
Probability of visiting Grand Tetons = 40%
Probability of visiting both = 35%

Probability of visiting at least one park = 50% + 40% - 35% = 55%

Therefore, the probability that a vacationer will visit at least one of these magnificent attractions is 0.55 or 55%.

Question 7

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 letters and we need to arrange them in a different order. So, the number of permutations is 3! which is equal to 6. Therefore, the answer is (C) 6.

Question 8

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)120...

Question 9

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 probability of selecting a woman for the first member of the search committee is 4/12. 
The probability of selecting another woman for the second member of the search committee is 3/11, since there are only 3 women remaining out of 11 people left. 
The probability of selecting a third woman for the third member of the search committee is 2/10. 
Finally, the probability of selecting the fourth woman for the fourth member of the search committee is 1/9. 
Therefore, the probability of selecting all four women is (4/12) x (3/11) x (2/10) x (1/9) = 1/495 or 0.002.

Question 10

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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

To find the probability of selecting a female who did NOT attend college, we need to first find the probability of selecting a female and then subtract the probability of selecting a female who did attend college.

Probability of selecting a female = 0.80
Probability of selecting a female who attended college = 0.80 * 0.90 = 0.72

Therefore, probability of selecting a female who did NOT attend college = 0.80 - 0.72 = 0.08, which is the answer choice B.

Question 11

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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

The probability of selecting a male is 20% or 0.20. The probability that a male did not attend college is 22% (100% - 78%). Therefore, the probability of selecting a male who did not attend college is 0.20 * 0.22 = 0.044.

Question 12

A gumball machine is filled with 50 black, 150 white, 100 red, and 100 yellow gumballs 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

There are a total of 400 gumballs in the machine. The probability of Sue selecting a red gumball is 100/400 or 1/4. After Sue selects a red gumball, there are 99 red gumballs left out of a total of 399 gumballs. Therefore, the probability of Jim selecting a red gumball after Sue has selected one is 99/399 or 11/47. The probability of both events occurring is the product of their individual probabilities: (1/4) x (11/47) = 11/188, which is approximately 0.062. Therefore, the likelihood (or probability) of both Sue and Jim getting red gumballs is 0.062 or 6.2%. Option B is the best choice.

Question 13

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 will be returned 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

The probability of the first toothbrush being defective is 3/20. If the first toothbrush is returned, the probability of the second toothbrush being defective is 2/19 (since there are now only 19 toothbrushes left and 2 of them are defective). Therefore, the probability of both toothbrushes being defective and returned is (3/20) * (2/19) = 3/190 or 0.01579.

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 simplifies to 4! / (4!0!) = 24 / 1 = 24.

Question 15

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 16

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

To find the total number of different systems, we need to multiply the number of options for each component together: 
4 types of receivers x 3 amplifiers x 6 speaker brands = 72 different systems. Thus, the answer is (C) 72.

Question 17

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

Since there are five possible free gifts, the probability of randomly 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 and removed from the options). Thus, the probability of selecting an umbrella and a shaving kit in that order is (1/5)*(1/4) = 0.05 or 5%.

Question 18

You have the assignment of designing color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used-such as green, yellow, and red-these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations, how many colors were available?
A)5
B)7
C)9
D)11

Accepted Answer

The number of combinations of colors can be found using the combination formula nCr = n! / [r!(n-r)!], where n is the total number of colors available, and r is the number of colors to be chosen (in this case, 3). Given 35 combinations, we solve for n in the equation 35 = n! / [3!(n-3)!]. Simplifying, we find that n = 7.

Question 19

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 20

A developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?
A)8
B)10
C)15
D)30

Accepted Answer

The number of different homes that can be built is the product of the number of interior plans and the number of exteriors, which is 3 * 5 = 15.

Quiz 5: A Survey of Probability Concepts

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, 20% male. A total of 90% of the females attended college, while 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 attend college?

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 attend college?

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 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?

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

What does equal?

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?

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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?

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 gumball machine is filled with 50 black, 150 white, 100 red, and 100 yellow gumballs that have been thoroughly mixed. Sue and Jim each purchased one gumball. What is the likelihood both Sue and Jim get red gumballs?

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 will be returned because they are defective?

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?

In a management trainee program, 80% of the trainees are female, 20% male. A total of 90% of the females attended college, while 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 developer of a new subdivision wants to build homes that are all different. There are three different interior plans that can be combined with any of five different home exteriors. How many different homes can be built?