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Are you Ready for the Quiz?

Are you Ready for the Quiz?. Yes No That depends on how you measure ‘readiness’. Upcoming In Class. Today Quiz 2, covers HW2 and HW3 of the material learned in class. (9/12) Sunday HW4 (9/16) Part 2 of the data project due next Monday (9/17). Chapter 14. From Randomness to Probability.

jason-velasquez
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Are you Ready for the Quiz?

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  1. Are you Ready for the Quiz? • Yes • No • That depends on how you measure ‘readiness’.

  2. Upcoming In Class • Today Quiz 2, covers HW2 and HW3 of the material learned in class. (9/12) • Sunday HW4 (9/16) • Part 2 of the data project due next Monday (9/17)

  3. Chapter 14 From Randomness to Probability

  4. Modeling Probability (cont.) • The probability of an event is the number of outcomes in the event divided by the total number of possible outcomes. P(A) = # of outcomes in A # of possible outcomes

  5. Formal Probability • Two requirements for a probability: • A probability is a number between 0 and 1. • For any event A, 0 ≤ P(A) ≤ 1. • Probability Assignment Rule: • The probability of the set of all possible outcomes of a trial must be 1. • P(S) = 1 (S represents the set of all possible outcomes.)

  6. Formal Probability (cont.) • Complement Rule: • The set of outcomes that are not in the event A is called the complement of A, denoted AC. • The probability of an event occurring is 1 minus the probability that it doesn’t occur: P(A) = 1 – P(AC)

  7. Formal Probability (cont.) • Addition Rule (cont.): • For two disjoint events A and B, the probability that one or the other occurs is the sum of the probabilities of the two events. • P(AorB) = P(A) + P(B),provided that A and B are disjoint.

  8. Formal Probability • Multiplication Rule (cont.): • For two independent events A and B, the probability that both A and B occur is the product of the probabilities of the two events. • P(AandB) = P(A) x P(B), provided that A and B are independent.

  9. Problem 5 • A consumer organization estimates that over a 1-year period 16% of cars will need to be repaired once, 7% will need repairs twice, and 1% will require three or more repairs. • Suppose you own two cars.

  10. What is the probability that neither car will need repaired this year? • .76 • .24 • .5776 • .0576

  11. What is the probability that BOTH cars will need repaired this year? • .76 • .24 • .5776 • .0576

  12. What is the probability that at least one car will need repaired this year? • .76 • .24 • .5776 • .4224

  13. Problem 9 - • For a certain candy, 10% of the pieces are yellow, 20% are blue, 20% are red, 10% are green, and the rest are brown. • If you pick a piece at random, calculate the probability of the following…

  14. What is the probability that you pick a brown piece? • 40% • 60% • .4 • .6

  15. What is the probability the piece you pick is yellow OR blue? • .1 • .3 • .7 • .9

  16. What is the probability the piece you pick is NOT green? • .1 • .2 • .8 • .9

  17. What is the probability the piece you pick is stripped? • 0 • .1 • .5 • 1

  18. Problem 9 • Now suppose you pick three pieces. • You observe three independent events.

  19. What is the probability of picking three brown candies? • .064 • .4 • .64 • .936 • 1.2

  20. What is the probability of third one being the first red? • 0.008 • 0.128 • 0.2 • 0.8

  21. What is the probability that none are yellow? • 0.001 • 0.729 • 0.9 • 0.999

  22. What is the probability of at least one green candy? • 0.1 • 0.271 • 0.729 • 0.9

  23. Problem 15 • On September 11, 2002, a particular state lottery’s daily number came up 9-1-1. Assume that no more than one digit is used to represent the first nine months.

  24. What is the probability that the winning three numbers match the date on any given day than can be represented by a three digit number? • 0.000 • 0.001 • 0.273 • 1

  25. What’s the probability that the winning three number match the date on any given day that can be represented by a 4-digit number? • 0.000 • 0.001 • 0.273 • 1

  26. What’s the probability that a whole year passes without the lottery number matching the day? • 0.001 • 0.694 • 0.761 • 0.999

  27. Upcoming In Class • Today Quiz 2, covers HW2 and HW3 of the material learned in class. (9/12) • Sunday HW4 (9/16) • Part 2 of the data project due next Monday (9/17)

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