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10.8 Probability Mon Dec 2

10.8 Probability Mon Dec 2. Do Now There are 52 cards in a deck of cards. How many different 5 card hands can you make? (every card is unique). Quick Review. 10.5 Permutations 10.6 Combinations 10.7 Binomial Theorem. Probability.

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10.8 Probability Mon Dec 2

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  1. 10.8 ProbabilityMon Dec 2 Do Now There are 52 cards in a deck of cards. How many different 5 card hands can you make? (every card is unique)

  2. Quick Review • 10.5 Permutations • 10.6 Combinations • 10.7 Binomial Theorem

  3. Probability • Probability is the chance, or likelihood that a certain event occurs • Probability is heavily dependent on combinatorics to determine what values are used

  4. Experimental Probability Experimental Probability is the likelihood of an event occurring based on actually conducting an experiment EX: Flipping a coin 1000 times; get heads 503 times. The experimental probability of getting heads is 503/1000

  5. Theoretical Probability • Theoretical Probability is the likelihood of an event occurring based on using mathematics, particularly combinatorics • EX: The theoretical probability of getting heads on a coin flip is 1/2

  6. Computing Experimental Probabilities • Given an experiment in which N observations are made, if a situation, or event, E occurs M times out of N observations, then we say that the experimental probability of the event, P(E), is given by P(E) = M / N

  7. Ex1 • An experimental survey was conducted to determine the number of people who are left-handed, right-handed, or both. Out of 100 people, 82 answered right-handed, 17 answered left-handed, and 1 answered both. • (A) Determine the probability that a person is right handed • (B) Determine the probability that a person is left-handed. • (C ) Out of 120 people, how many would we expect to be left-handed?

  8. Ex 2 • The Department of Agriculture requires that 80% of the seeds that a company produces must sprout. To determine the quality of the seeds it produces, a company takes 500 seeds and plants them. It finds that 417 of the seeds sprout. • (A) What is the probability that a seed will sprout? • (B) Did the seeds meet government standards?

  9. Ex 3 • There are an estimated 110,200,000 households with televisions in the US. One week, 12,077,000 households tuned in to “60 Minutes” and 10,672,000 households tuned in to “Lost.” • (A) What is the probability that a household tuned in to 60 Minutes? • (B) What is the probability that a household tuned in to Lost?

  10. Closure • What is experimental probability? What are the pros and cons to using experimental probability? • HW: p.914 #1-5 odds (need to fill out #4 to answer #5)

  11. Theoretical ProbabilityTues Dec 3 • Do Now • A box of gumdrops was opened and there were 9 orange, 8 lemon, 7 strawberry, 6 grape, 5 lime, and 4 cherry gumdrops. If we take one gumdrop out of the box, what is the probability of getting a lemon? A lime? A grape?

  12. HW Review p.914 #1-5

  13. Theoretical Probability • In experimental probability, each possible result is called an outcome • The set of all possible outcomes is called the sample space • An eventis a set of outcomes

  14. Theoretical Probability • If an event E can occur M ways out of N possible equally likely outcomes of a sample space, then the theoretical probability of the event P(E) is given by P(E) = M / N

  15. Probability Properties • 1) If an event E cannot occur, then P(E) = 0 • 2) If an event E is certain to occur, then P(E) = 1 • 3) The probability that an event E will occur must be a number from 0 to 1

  16. Ex1 • What is the probability of rolling a 3 on a die?

  17. Ex2 • What is the probability of rolling an even number on a die?

  18. Ex 3 • What is the probability of drawing an ace from a deck of 52 cards?

  19. Ex4 • Suppose we select, without looking, one marble from a bag containing 3 red marbles and 4 green marbles. What is the probability of selecting a red marble?

  20. Ex5 • Suppose that 2 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that both are spades?

  21. Ex6 • Suppose that 3 people are selected at random from a group that consists of 6 men and 4 women. What is the probability that 1 man and 2 women are selected?

  22. Ex 7 • What is the probability of getting a total of 8 on a pair of dice?

  23. Closure • Suppose that 5 cards are drawn from a deck of 52 cards. (Note: order does NOT matter) What is the probability of drawing 4 aces and 1 five? • HW: p.915 #7-23 odds

  24. Theoretical Probability Cont’dWed Dec 4 • Do Now • The sales force of a business consists of 10 men and 10 women. A production unit of 4 people is set up at random. What is the probability that 2 men and 2 women are chosen?

  25. HW Review: p.915 #7-23

  26. Probability Property • If you want the probability of AT LEAST one type of event happening, the easiest way to calculate that is: • (A) Find the probability that no events happen • (B) Subtract the probability of A from 1

  27. Same birthday probability

  28. Closure • What is the difference between experimental and theoretical probability? • HW: none

  29. 10.8 More ProbabilityThurs • Do Now • Suppose that 5 cards are drawn from a deck of 52 cards. What is the probability of drawing an ace high straight? (10-J-Q-K-A)

  30. Poker Discussion

  31. Poker Activity

  32. Closure • If we use today’s activity to calculate probability, would we use experimental or theoretical probability? Would it be a good idea? • HW: p.917 #37-43 odds

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