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AP Statistics Review

AP Statistics Review. Probability(C14-C17 BVD) C14: Introduction to Probability. Probability - long-run relative frequency of an event. Trial – A single attempt or realization of a random phenomenon. Outcome – the value measured or observed for a single trial or a random event.

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AP Statistics Review

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  1. AP Statistics Review Probability(C14-C17 BVD) C14: Introduction to Probability

  2. Probability - long-run relative frequency of an event. • Trial – A single attempt or realization of a random phenomenon. • Outcome – the value measured or observed for a single trial or a random event. • Event – A collection of outcomes of interest. • Independent events – knowing whether one event occurs does not alter the probability of the other event occurring. Probability Vocabulary

  3. The long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency as the number of trials increases. • If the true relative frequency of an event is 0.5, getting 4/10 is not that unusual. Getting 400/1000 is more unusual. • Many people mistakenly behave as if the Law of Averages held true, but it does not. Long streaks of a particular outcomes can and do happen even if the streak seems to defy the true relative frequency. (Gambling behavior, etc.) Law of Large Numbers

  4. P(event) = probability of event occurring. • Probabilities are between 0 and 1. • S = Sample Space – set of all events that can occur • Complement Rule = A very handy rule, it says the probability of event happening is 1 minus the probability of anything else happening. • U = union – P (A U B) = P (A or B) in a single event = P(A) + P(B) if there is no overlap between A and B. • Disjoint/mutually exclusive – events that have no overlap are disjoint or mutually exclusive. Think Venn Diagram with circles that have no outcomes in common. • Upside down U – intersection – P(A intersection B) = P(A and B) in two concurrent or consecutive trials = P(A) * P(B). Probability Notation and Rules

  5. The American Red Cross says 45% of Americans have Type O blood, 40% Type A, 11% Type B and the rest Type AB • What is the probability that a donor… • 1. has type AB? • 2. has type A or B? • 3. Is not Type O? • If there are 4 donors waiting to donate, what is the probability that… • 1. all are type O? • 2. none are type AB? • 3. they are not all type A? • 4. at least one person is type B? Example

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