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Chapter 8

Chapter 8. Review Problems And Solutions. Problem #1.

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Chapter 8

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  1. Chapter 8 Review Problems And Solutions

  2. Problem #1 • Given a group of 5 male students and 4 female students, count the different ways of choosing a president, vice president, and secretary if the president must be a male and the other two must be female. Assume that no one can hold more than one office.

  3. Solution to Problem #1 5 x 4 x 3 = 60 Pres. Vice Pres. Sec.

  4. Problem #2 • Evaluate the following by showing all formula work. P(12, 3)

  5. Solution to Problem #2 P(12, 3) nPr = __n!__ (n - r)! 12P3 = __12!__ = 12! = 12·11·10·9! (12 - 3)! 9! 9! = 12·11·10 = 1320

  6. Problem #3 • A bookshelf contains 10 novels: 6 mysteries and 4 romances. If three books are selected without looking, how many ways can you get exactly 2 mysteries?

  7. Solution to Problem #3 Want 2 mysteries and 1 romance novel. 6C2 ·4C1 = 60

  8. Problem #4 • A class has 15 boys and 10 girls. In how many ways can a committee of five be selected if the committee can have at most two girls?

  9. Solution to Problem #4 Can have 0 girls or 1 girl or 2 girls. 10C0·15C5 + 10C1·15C4 + 10C2·15C3 = 37,128

  10. Problem #5 • Find the probability of a bridge hand that has exactly 3 kings, exactly 2 queens, and exactly 1 ace. A bridge hand consists of 13 cards dealt from a standard deck of 52.

  11. Solution to Problem #5 You want 3 kings, 2 queens, 1 ace and 7 other cards in your hand. The sample space is 52C13. 4C3· 4C2· 4C1· 40C7≈ .003 52C13

  12. Problem #6 • A family has six children. The probability of having a girl is .5. What is the probability of having 4 boys and 2 girls?

  13. Solution to Problem #6 n = 6 success: girl x = 2 p (girl) = .5 6C2 (.5)² (.5) ≈ .234 4

  14. Problem #7 • Prepare a probability distribution for the experiment below. Three cards are drawn from a deck. The number of fives are counted.

  15. Solution to Problem #7

  16. Problem #8 • Three rats are inoculated against a disease. The number contracting the disease is noted and the experiment is repeated 50 times. Create a probability distribution and find the expected number of rats contracting the disease.

  17. Solution to Problem #8 E(x) = 0(.24) + 1(.40) + 2(.26) + 3(.10) = 1.22 The expected number of rats in 50 that will contract the disease is 1.22.

  18. Problem #9 • Find the expected number of boys in a family of three.

  19. Solution to Problem #9 This is a binomial probability problem, so the shortcut formula E(x) = np can be used. n = 3 p (boy) = .5 E(x) = 3(.5) = 1.5 You should expect 1.5 boys in a family of three.

  20. Problem #10 • A car buyer has an option between an automatic or manual transmission in a certain make of car that he has decided to purchase. The car comes in one of 5 different colors, with or without a moonroof, and with one of three special options packages. How many options does the car buyer have when choosing the car he wants to buy?

  21. Solution to Problem #10 There are four different decisions to make: transmission, color, moonroof, and options package. 2 x 5 x 2 x 3 = 60

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