Question 1

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

We can use the formula for conditional probability to solve this problem. Let M represent the event that the selected trainee is male, and C represent the event that they attended college. We want to find the probability of selecting a male who did not attend college, which is P(M and not C). This can be calculated as:
P(M and not C) = P(M) * P(not C|M)
We already know that P(M) = 0.2. To find P(not C|M), we need to use the formula:
P(not C|M) = (P(not C and M)) / P(M)
We can find P(not C and M) by using the complement rule:
P(not C and M) = 1 - P(C and M)
We know that P(C and M) = P(M) * P(C|M) = 0.2 * 0.22 = 0.044, since 22% of the males attended college. Therefore, P(not C and M) = 1 - 0.044 = 0.956. Plugging this into the formula for P(not C|M), we get:
P(not C|M) = 0.956 / 0.2 = 4.78.
Finally, we can combine this with P(M) to get the overall probability of selecting a male who did not attend college:
P(M and not C) = P(M) * P(not C|M) = 0.2 * 4.78 = 0.044, which is choice (A).

Question 2

You have the assignment of designing color codes for different parts.Three colors are used on each part,but a combination of three colors used for one part cannot be rearranged and used to identify a different part.This means that if green,yellow and violet were used to identify a camshaft,yellow,violet and green (or any other combination of these three colors)could not be used to identify a pinion gear.If there are 35 combinations,how many colors were available?
A)5
B)7
C)9
D)11

Accepted Answer

To determine the number of available colors, we need to find the number of unique combinations of three colors that can be made from those colors. We can use the formula for combinations, which is:

nCr = n! / r!(n-r)!

where n is the total number of colors and r is the number of colors in each combination.

We know that there are 35 combinations, so we can set up an equation:

nC3 = 35

n! / (3!*(n-3)!) = 35

Expanding the factorials and simplifying, we get:

n(n-1)(n-2) / 6 = 35

n(n-1)(n-2) = 210

By trial and error, we can find that n = 7 satisfies this equation. Therefore, there were 7 available colors to choose from.

Question 3

How many permutations of the two letters C and D are possible?
A)1
B)0
C)4
D)8

Accepted Answer

There are 2 letters and we are arranging them in a line, so the number of permutations is simply 2 factorial, or 2! = 2 x 1 = 2. We have CD and DC as possible arrangements, which gives us 2 permutations. Therefore, the answer is C) 4 is the best choice.

Question 4

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 5

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 6

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 7

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 attractions, we need to add the probabilities of visiting Yellowstone Park, Grand Tetons, or both. 
P(Yellowstone) = 0.50 
P(Grand Tetons) = 0.40 
P(Both) = 0.35 
To find the probability of visiting at least one, we can use the formula: 
P(Yellowstone or Grand Tetons) = P(Yellowstone) + P(Grand Tetons) - P(Both) 
= 0.50 + 0.40 - 0.35 
= 0.55 
Therefore, the probability that a vacationer will visit at least one of these attractions is 0.55 or 55%.

Question 8

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 choosing a woman from the board of directors is 4/12 (=1/3) since four out of twelve members are women. Therefore, the probability of choosing four women in a row can be calculated by multiplying the probability of choosing a woman each time.
(4/12) x (3/11) x (2/10) x (1/9) = 1/495 or 0.002. 
Hence the option D is correct.

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 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 answer of In a management trainee program,80 percent of...

Question 10

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 of...

Question 11

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 toothbrushes, of which 3 are defective. Therefore, the probability that the first toothbrush sold is defective is 3/20. Once the first toothbrush is sold, there will be 2 defective toothbrushes left out of 19 toothbrushes. Therefore, the probability that the second toothbrush sold is defective given that the first was defective is 2/19. Multiplying these probabilities, we get (3/20)*(2/19) = 3/190 or 0.01579. Therefore, the correct answer is D.

Question 12

A builder has agreed NOT to build all "look alike" homes in a new subdivision.The builder has three different interior plans that can be combined with any of the five different home exteriors.How many different homes can be built?
A)8
B)10
C)15
D)30

Accepted Answer

The answer of A builder has agreed NOT to build...

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 female who did NOT attend college?
A)0.20
B)0.08
C)0.25
D)0.80

Accepted Answer

Out of all the Trainees:
- 80% are female, which means 20% are male
- 90% of females attended college, which means 10% of females did not attend college
- 78% of males attended college, which means 22% of males did not attend college

To find the probability of selecting a female who did not attend college:
P(Female and did not attend college) = P(Female) x P(did not attend college | Female)
= 80% x 10%
= 8%
Therefore, the probability that the person selected is a female who did NOT attend college is 0.08.

Question 14

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 answer of The numbers 0 through 9 are used...

Question 15

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

To find the number of different systems the electronics firm can offer, we need to multiply the number of options for each component together: 4 stereo receivers x 3 CD decks x 6 speaker brands = 72 possible systems. Therefore, the answer is choice C, 72.

Question 16

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

The number of possible arrangements is equal to the number of lamp bases multiplied by the number of lampshades, which is 5 x 4 = 20. Therefore, the best choice is D.

Question 17

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

The probability of selecting a female who attended college is:
P(female and college) = P(female) x P(college|female) 
= 0.8 x 0.9 = 0.72 
Therefore, the answer is D) 0.72.

Question 18

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.
Once the Sue gets the red gumball, Jim's probability of getting red is 99/399 (as one red gumball has been already taken out). 
So the probability of both Sue and Jim getting red is (0.25)*(99/399)=0.062. Hence the answer is B.

Question 19

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 are given that 80% of the trainees are female and 90% of the females attended college. Therefore, the probability of selecting a female who attended college is 0.8 x 0.9 = 0.72. This is represented by P(did attend college | female). Therefore, the probability that the person selected is a female who did attend college is P(female) x P(did attend college | female), which is 0.8 x 0.72 = 0.576 or 57.6%.

Question 20

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 a defective roll on the first try is 3/10. After one roll is removed, there are 9 rolls left with 2 defective rolls remaining. So the probability of selecting another defective roll is 2/9. To find the probability of both events happening, we multiply the probabilities together:
3/10 * 2/9 = 1/15 or about 0.07. Therefore, the answer is choice D.

Quiz 5: A Survey of Probability Concepts

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

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?

What does equal?

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 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?

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 builder has agreed NOT to build all "look alike" homes in a new subdivision.The builder has three different interior plans that can be combined with any of the five different home exteriors.How many different homes can be built?

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 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 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?

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?