Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Attached is our project on basic probability. Please complete to best of your ab

ID: 3244158 • Letter: A

Question

Attached is our project on basic probability.

Please complete to best of your ability - for this submission, please show work as required by scanning as a Word or pdf document - with the Excel printouts as part of the one file.

For the combination and permutation questions, I encourage you to use Excel or similar software.

True / False Questions: please reply to 8 of your choice – if it is false, pleased provide a brief reason why.

1.

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

True    False

2.

The probability of rolling a 3 or 2 on a single die is an example of mutually exclusive events.

True    False

3.

An individual can assign a subjective probability to an event based on the individual's knowledge about the event.

True    False

4.

To apply the special rule of addition, the events must be mutually exclusive.

True    False

5.

A joint probability measures the likelihood that two or more events will happen concurrently.

True    False

6.

The joint probability of two independent events, A and B, is computed as P(A and B) = P(A) P(B).

True    False

7.

The joint probability of two events, A and B, that are not independent is computed as P(A and B) = P(A) P(B|A).

True    False

8.

A coin is tossed four times. The joint probability that all four tosses will result in a head is ¼ or 0.25.

True    False

9.

If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both.

True    False

10.

A combination of a set of objects is defined by the order of the objects.

True    False

11.

The complement rule states that the probability of an event not occurring is equal to one minus the probability of its occurrence.

True    False

12.

If two events are mutually exclusive, then P(A and B) = P(A)P(B).

True    False

Multiple Choice – please reply to 6 of your choice – you need not show work

1.

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

2.

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

3.

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

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

5.

What does 6!2! / 4!3! equal?

A.

640

B.

36

C.

10

D.

120

6.

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

7.

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

8.

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

9.

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)

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 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)

PERMUTATIONS AND COMBINATIONS please reply to 2 of your choice – you need not show work

1.

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

2.

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

3.

Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color, and touches of white. Another unit might have blue as the principal color, white as the complementary color, gold as the accent color, and touches of red. If repetitions are permitted, how many different units can be decorated?

A.

7,825

B.

25

C.

125

D.

1,296

4.

A rug manufacturer has decided to use seven compatible colors in her rugs. However, in weaving a rug, only five spindles can be used. In advertising, the rug manufacturer wants to indicate the number of different color groupings for sale. How many color groupings using the seven colors taken five at a time are there? (This assumes that five different colors will go into each rug—in other words, there are no repetitions of color.)

A.

7

B.

21

C.

840

D.

42

MUTUALLY EXCLUSIVE/ MISC please reply to 4 of your choice – you need not show work

1.

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.

                    Potential for Advancement

                                                 Fair                    Good                  Excellent

                     Below Average    16                       12                      22

Sales Ability Average                45                      60                     45

                     Below Average     93                      72                    135

  What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

A.

0.09

B.

0.12

C.

0.30

D.

0.525

2.

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.

                    Potential for Advancement

                                                 Fair                    Good                  Excellent

                     Below Average    16                       12                      22

Sales Ability Average                45                      60                     45

                     Below Average     93                      72                    135
  

What is the probability that a salesperson selected at random will have below average sales ability and fair potential for advancement?

A.

0.032

B.

0.10

C.

0.16

D.

0.32

3.

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.

Potential for Advancement

                                                 Fair                    Good                  Excellent

                     Below Average    16                       12                      22

Sales Ability Average                45                      60                     45

                     Below Average     93                      72                    135



What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have above average sales ability?

A.

0.27

B.

0.60

C.

0.404

D.

0.45

4.

Each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. The data for the 500 sampled salespeople are summarized in the following table.

Potential for Advancement

                                                 Fair                    Good                  Excellent

                     Below Average    16                       12                      22

Sales Ability Average                45                      60                     45

                     Below Average     93                      72                    135



What is the probability that a salesperson selected at random will have an excellent potential for advancement given they also have average sales ability?

A.

0.27

B.

0.30

C.

0.404

D.

0.45

5.

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:


What is the probability that a designer does not prefer red?

A.

1.00

B.

0.77

C.

0.73

D.

0.23

6.

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:

Primary Color         Number of Opinions

Red                         92

Orange                   86

Yellow                    46

Green                     91

Blue                        37

Indigo                    46

Violet                      2

What is the probability that a designer does not prefer yellow?

A.

0.000

B.

0.765

C.

0.885

D.

1.000

7.

A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:

Primary Color         Number of Opinions

Red                         92

Orange                   86

Yellow                    46

Green                     91

Blue                        37

Indigo                    46

Violet                      2

  

What is the probability that a designer does not prefer blue?

A.

1.0000

B.

0.9075

C.

0.8850

D.

0.7725

1.

The probability of rolling a 3 or 2 on a single die is an example of conditional probability.

True    False

Explanation / Answer

1)
False
Conditional probability examines the probability of one event based on the occurrence of another event and returns their product (a * b). The probability of rolling a 3 in a single die does not affect the probability of rolling a 2 in a single die.


2)
True

3)
True

4)
True

5)
True

6)
True

7)
True

9)
True

11)
True

12)
false
If two events are mutually exclusive, then P(A and B) = 0
If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.