Understanding Probability and Experiment Outcomes

1. 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%)