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A situation involving uncertain results is called an experiment. The set of all possible outcomes of an experiment is called the sample space. The Probability of an event is the relative frequency with which it can be expected to occur. A subset of the sample space is called an event.
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A situation involving uncertain results is called an experiment. • The set of all possible outcomes of an experiment is called the sample space. • The Probability of an event is the relative frequency with which it can be expected to occur. • A subset of the sample space is called an event. • What does the Law of Large Numbers say? The more often you repeat an experiment the closer the relative frequency of an event is to the theoretical probability. • If the probability of event A does not change when you know B has occurred, then A and B are independent. • If events A and B cannot both occur they are Mutually Exclusive. Problems: The probability of rolling a 3 on a standard 6-sided fair die is 1/6 The probability of rolling an even number on a standard 6-sided fair die is 1/2 Can the probability of an event be 2? No 0 < P(A) < 1 If you flip two coins, a penny and a dime and the dime is a head, what is the probability that you have two heads? 1/2 If you flip two coins, a penny and a dime and one of them is a head, what is the probability that you have two heads? 1/3 If 3% of a given population uses drugs and you use a drug test that returns an accurate result 90% of the time, what is the probability that a person taken at random tests positive? (.03)(.90) + (.97)(.1) = .027 + .097 = .124 (12.4%) In the same situation as above, if a person randomly chosen tests positive, what is the probability that he/she is a drug user? .027 / .124 = (approx) .218 (< 22%)
