# Input-Output Matrices, Probability, Matrix Inverses, Probability Distributions and Transition Matrices

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1. For the input-output matrix A, and the output matrix X, of three industries, find the amounts consumed internally by the production process.

0.10 0.15 0.10 500

A = 0.20 0.05 0.08 X = 800

0.04 0.06 0.02 400

2. For the input-output matrix A, and the output matrix X, of three industries, find the amounts consumed internally by the production process.

0.15 0.25 0.10 1000

A = 0.05 0.05 0.12 X = 2000

0.12 0.16 0.08 2500

3. Of 200 students surveyed 40 subscribe to Time Magazine, 65 subscribe to Sports Illustrated, and 10 subscribe to both. If a student is selected at random, what is the probability the student subscribes to Time Magazine or Sports Illustrated?

4. For two events E and F, P(E) = 0.36, P(F) = 0.48, and P(the intersection of E and F) = 0.08. P(F|E) = ____.

5. The probability that Andy studies math over break is 0.3 and the probability that Betty independently studies over break is 0.4. Find the probability Andy studies math over break and Betty doesn't.

6. In a group of 100 college freshmen, 25 lettered in band, 20 were in the honor society, and 5 lettered in band were in the honor society. Determine if the events "letter in band" and "in the honor society" are independent.

7. E and F are independent with P(E) = 0.35 and P(F) = 0.45. P(the union of E and F) = _____.

8. P(E_1) = 0.25, P(E2) = 0.75, P(F|E1) = 0.05, P(F|E2) = 0.12. P(E2|F) = ____.

8. One printing shop charges $5 plus $0.02 per page and a second shop charges $7 plus $0.015 per page. If _____ pages are printed, the total cost is less for the first printing shop.

9. The solution to the system of equations below is

3x + 4y = -6

x - 5y = 17

10. The system below has _____ solutions.

11. The augmented matrix for the system of equations below is

3x - 2y = 5

4x + 7y = 2

15. The following matrix is obtained from a system of equations

1 0 6 5

0 1 -4 3

0 0 2 -6

The solution to the system is ____.

16.

3 2 1 + 2 -3 5 =

4 0 1 1 7 6

17.

A = 5 1 B = -1 3 Find A - 2B

3 2 4 1

18. The size of the matrix 3 1 4 is

2 0 2

1 1 1

-2 4 3

19. The dot product [3 1 4] * 2 is

-1

5

20. The inverse of 1 -1 0 is

0 1 1

1 0 -1

21. A number is drawn at random from the numbers 1 through 20. The probability the number is a multiple of 3 is

22. P(E) = 0.30, P(F) = 0.40, P(The intersection of E and F) = 0.1, P(The union of E and F) = ____.

23. A computer store has 10 copies of a word processing program, 12 copies of a spread sheet program, and 8 copies of a draw program. Three of the word processing, four of the spread sheet and two of the draw programs are infected with a computer virus. If a program is selected at random, the probability it is infected with a virus is _____.

24. For the input-output matrix A, find the output required to meet the demand D.

25. For the input-output matrix A, find the output required to meet the demand D.

26. One urn contains 3 red and 7 white marbles. A second urn contains 2 red and 8 white marbles. One urn is selected and a ball drawn. The probability of selecting the first urn is 0.4 and the probability of selecting the second is 0.6. If a white ball is drawn, find the probability it came from the second urn.

27. The expected value of the following probability distribution is

x_i 1 5 10 20 50

p_i 0.3 0.40 0.10 0.15 0.05

28. The probability a basketball player makes a free throw is 0.60. Find the probability the player makes four out of 6.

29. In a binomial distribution, the probability of 25 successes, where n = 65 and p = 35 is ______.

30. For a score = 140, mean = 150, sigma = 4, z = ____.

31. In order for 0.3 0.2 0.5 to be a transition matrix x =_.

0.1 0.6 0.3

0.7 x 0.3

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Input-Output Matrices, Probability, Matrix Inverses, Probability Distributions and Transition Matrices are investigated. The solution is presented in an attached Word document.

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