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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 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)
Quick Review • 10.5 Permutations • 10.6 Combinations • 10.7 Binomial Theorem
Probability • Probability is the chance, or likelihood that a certain event occurs • Probability is heavily dependent on combinatorics to determine what values are used
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
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
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
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?
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?
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?
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)
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?
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
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
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
Ex1 • What is the probability of rolling a 3 on a die?
Ex2 • What is the probability of rolling an even number on a die?
Ex 3 • What is the probability of drawing an ace from a deck of 52 cards?
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?
Ex5 • Suppose that 2 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that both are spades?
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?
Ex 7 • What is the probability of getting a total of 8 on a pair of dice?
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
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?
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
Closure • What is the difference between experimental and theoretical probability? • HW: none
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)
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