Probability(C14-C17 BVD)

C14: Introduction to Probability

*AP Statistics Review

Probability Vocabulary

*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.

*Law of Large Numbers

*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.)

*Probability Notation and

Rules

*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).

*Example

*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?