Stats 3y03 assignment 1 PDF

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STATS 3Y03 ASSIGNMENT 1Problem #1: In the layout of a printed circuit board for an electronic product, 15 different locations can accommodate chips.(a) If 6 chips of different types are to be placed on the board, how many different layouts are possible? (b) If all of the locations are to be filled w...

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STATS 3Y03 ASSIGNMENT 1 Problem #1: In the layout of a printed circuit board for an electronic product, 15 different locations can accommodate chips. (a) If 6 chips of different types are to be placed on the board, how many different layouts are possible? (b) If all of the locations are to be filled with chips, 4 of which are of one type, 5 of which are another type, and all others different, how many different layouts are possible? (c) If 6 chips of the same type are to be placed on the board, how many different layouts are possible? Correct Answer: 3603600 Problem #1(a): 3603600

Your Mark: 1/1 Correct Answer: 454053600 Problem #1(b): 454053600

Your Mark: 1/1 Correct Answer: 5005 Problem #1(c): 5005

Your Mark: 1/1 Problem #1 Your Answer:

Your Mark:

Problem #2:

Attempt #1

Attempt #2

1(a) 5005 1(b) 454053600 1(c) 4633200

1(a) 3603600 1(b) 1(c) 5005

1(a) 0/1✘ 1(b) 1/1 ✔ 1(c) 0/1✘

1(a) 1/1 ✔ 1(b) 1(c) 1/1 ✔

Consider the Venn diagram given to the right. In each part, determine which of the regions correspond to the given statements.

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(a) C′ ∩ (A ∩ B)′ (b) (A   B) ∩ C (c) A′ ∩ C′ (d) A    B

(A) Regions 6,8 (B) Regions 1,2,4,5,7 (C) Region 3 (D) Regions 1,2,3,4,5 (E) Regions 2,4,5 (F) Regions 1,6,8 Problem #2(a): F

(G) Regions 1,2,3,4,7,8 (H) Regions 1,2,3,4,5,6 ↑ Part (a) choices.

Correct Answer: F Your Mark: 1/1

(A) Regions 2,4,5 (B) Regions 6,8 (C) Regions 1,2,3,4,5 (D) Regions 1,2,4,5,7 (E) Regions 1,2,3,4,7,8 (F) Regions 1,6,8 (G) Regions 1,2,3,4,5,6 (H) Region 3 ↑ Part (b) choices. Problem #2(b): A

Correct Answer: A Your Mark: 1/1

(A) Region 3 (B) Regions 2,4,5 (C) Regions 1,6,8 (D) Regions 1,2,3,4,7,8 (E) Regions 1,2,3,4,5,6 (F) Regions 1,2,3,4,5 (G) Regions 1,2,4,5,7 (H) Regions 6,8 ↑ Part (c) choices. Problem #2(c): H

Correct Answer: H Your Mark: 1/1

(A) Region 3 (B) Regions 1,2,4,5,7 (C) Regions 1,2,3,4,5,6 (D) Regions 1,6,8 (E) Regions 2,4,5 (F) Regions 6,8 (G) Regions 1,2,3,4,5 (H) Regions 1,2,3,4,7,8 ↑ Part (d) choices. Problem #2(d): C

Correct Answer: C Your Mark: 1/1 Problem #2 Your Answer:

Your Mark:

Attempt #1

Attempt #2

2(a) F 2(b) A 2(c) H 2(d) C

2(a) 2(b) 2(c) 2(d)

2(a) 1/1 ✔ 2(b) 1/1 ✔ 2(c) 1/1 ✔ 2(d) 1/1 ✔

2(a) 2(b) 2(c) 2(d)

Problem #3: A manufacturer of front lights for automobiles tests lamps under a high-humidity, high-temperature environment using intensity and useful life as the responses of interest. The following table shows the performance of 133 lamps. Useful Life Intensity Satisfactory Unsatisfactory

Satisfactory Unsatisfactory 100 6 10

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Suppose that one of the above lamps is randomly selected. Let A be the event that is has a satisfactory useful life and let B be the event that it has a satisfactory intensity. Calculate the following probabilities. (a) P( A′   B) (b) P( A ′∩ B) (c) P( A ∩ B) (d) P(A) × P(B) Correct Answer: 123/133 Problem #3(a): 123/133

Your Mark: 1/1 Correct Answer: 6/133 Problem #3(b): 6/133

Your Mark: 1/1 Correct Answer: 100/133 Problem #3(c): 100/133

Your Mark: 1/1 Correct Answer: 11660/17689 Problem #3(d): 0.72757

Your Mark: 0/1 Problem #3

Attempt #1

Attempt #2

Your Answer:

3(a) 123/133 3(b) 6/133 3(c) 100/133 3(d) 0.659

3(a) 3(b) 3(c) 3(d) 0.72757

3(a) 1/1 ✔ 3(b) 1/1 ✔ 3(c) 1/1 ✔ 3(d) 0/1✘

3(a) 3(b) 3(c) 3(d) 0/1✘

Your Mark:

Problem #4: Suppose that a code (similar to a postal code) is of the form LDL DLD, where 'L' is an uppercase letter from A to N (i.e., 14 possible letters) and 'D' is a digit from 0 to 5. Suppose that such a code is randomly generated. (a) Find the probability that the code has no repeated digits. (b) Find the probability that the code either starts with an 'A' or ends with an even digit (note that 0 is even). (c) Find the probability that the code starts with an 'A' and does not contain any 'B's. Correct Answer: 5/9 Problem #4(a): 0.442176

Your Mark: 0/1 Correct Answer: 15/28 Problem #4(b): 0.535714

Your Mark: 1/1 Correct Answer: 169/2744 Problem #4(c): 0.061588

Your Mark: 1/1 Problem #4

Attempt #1

Attempt #2

Your Answer:

4(a) 0.795918 4(b) 0.535714 4(c) 0.061588

4(a) 0.442176 4(b) 4(c)

4(a) 0/1✘ 4(b) 1/1 ✔

4(a) 0/1✘ 4(b) 4(c)

Your Mark:

4(c) 1/1 ✔

Problem #5: A maintenance firm has gathered the following information regarding the failure mechanism for air conditioning systems. Gas Leaks Yes No Evidence of

Yes

78

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electrical failure

No

28

7

If this is a representative sample of AC failure, find the following probabilities. (a) That there was a gas leak, given that there was evidence of electrical failure. (b) That there was evidence of electrical failure, given that there was a gas leak. (c) Let A be the event that there is a gas leak and let B be the event that there is evidence of electrical failure. Find P(A′ | B). Correct Answer: 39/47 Problem #5(a): 0.82978

Your Mark: 1/1 Correct Answer: 39/53 Problem #5(b): 0.73584

Your Mark: 1/1 Correct Answer: 8/47 Problem #5(c): 0.090379

Your Mark: 0/1 Problem #5

Attempt #1

Attempt #2

Your Answer:

5(a) 0.82978 5(b) 0.73584 5(c) 0.05889

5(a) 5(b) 5(c) 0.090379

5(a) 1/1 ✔

5(a) 5(b) 5(c) 0/1✘

Your Mark:

5(b) 1/1 ✔ 5(c) 0/1✘

Problem #6: A production facility employs 16 workers on the day shift, 12 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to randomly select 7 of these workers for in-depth interviews. (a) What is the probability that all 7 selected workers will be from the same shift? (b) What is the probability that at least two different shifts will be represented among the selected workers? (c) What is the probability that exactly 3 of the workers in the sample come from the day shift? Correct Answer: 386/394383 Problem #6(a): 0.0009787

Your Mark: 1/1 Correct Answer: 393997/394383 Problem #6(b): 0.99902

Your Mark: 1/1 Correct Answer: 1225/3774 Problem #6(c): 0.324589

Your Mark: 1/1 Problem #6

Attempt #1

Attempt #2

Your Answer:

6(a) 0.0009787 6(b) 0.99902 6(c) 0.00209

6(a) 6(b) 6(c) 0.324589

6(a) 1/1 ✔

6(a) 6(b) 6(c) 1/1 ✔

Your Mark:

6(b) 1/1 ✔ 6(c) 0/1✘

Problem #7: A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that

P(A1) = 0.36, P(A2) = 0.4, P(A3) = 0.46, P(A1    A2) = 0.66, P(A1    A3) = 0.68, P(A2    A3) = 0.72, P(A1 ∩ A2 ∩ A3) = 0.04 (a) Find the probability that the system has exactly 2 of the 3 types of defects. https://www.childsmath.ca/childsa/forms/3yStuff/onlineform_2.php?assign=1

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(b) Find the probability that the system has a type 1 defect given that it does not have a type 2 or type 3 defect. Problem #7(a):

0.26 Correct Answer: 0.26

Your Mark: 1/1 Correct Answer: 0.5714 Problem #7(b): 0.57142

Your Mark: 1/1 Problem #7

Attempt #1

Attempt #2

Your Answer:

7(a) 0.26 7(b) 0.285714

7(a) 7(b) 0.57142

7(a) 1/1 ✔

7(a) 7(b) 1/1 ✔

Your Mark:

7(b) 0/1✘

Problem #8: Heart failures are due to either natural occurrences (89%) or outside factors (11%). Outside factors are related to induced substances (72%) or foreign objects (28%). Natural occurrences are caused by arterial blockage (51%), disease (26%), and infection (23%). (a) Determine the probability that a faliure is due to an induced substance. (b) Determine the probability that a failure is due to disease or infection. Correct Answer: 0.0792 Problem #8(a): 0.0792

Your Mark: 1/1 Correct Answer: 0.4361 Problem #8(b): 0.4361

Your Mark: 1/1 Problem #8

Attempt #1

Attempt #2

Your Answer:

8(a) 0.0792 8(b) 0.6586

8(a) 8(b) 0.4361

8(a) 1/1 ✔ 8(b) 0/1✘

8(a) 8(b) 1/1 ✔

Your Mark:

Problem #9: A lot of 109 semiconductor chips contains 15 that are defective. (a) Two are selected, one at a time and without replacement from the lot. Determine the probability that the second one is defective. (b) Three are selected, one at a time and without replacement. Find the probability that the first one is defective and the third one is not defective. Correct Answer: 15/109 Problem #9(a): 0.1376146

Your Mark: 1/1 Correct Answer: 235/1962 Problem #9(b): 0.11977573

Your Mark: 1/1 Problem #9

Attempt #1

Your Answer:

9(a) 0.1376146 9(b) 0.11977573

9(a) 9(b)

9(a) 1/1 ✔

9(a) 9(b)

Your Mark:

9(b) 1/1 ✔

Attempt #2

Problem #10: Suppose that an operating room needs to schedule 3 knee, 5 hip, and 4 shoulder surgeries. Assume that all schedules are equally likely. (a) Find the probability that all of the knee surgeries are completed first. (b) Find the probability that the schedule begins with a hip surgery, given that all of the shoulder surgeries are last. Correct Answer: 1/220 Problem #10(a): 1/220

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5/6

Your Mark: 1/1 Problem #10(b):

Correct Answer: 5/8 5/8

Your Mark: 1/1

Problem #10

Attempt #1

Attempt #2

Your Answer:

10(a) 1/220 10(b) 3/8

10(a) 10(b) 5/8

Your Mark:

10(a) 1/1 ✔ 10(b) 0/1✘

10(a) 10(b) 1/1 ✔

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