1. 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.

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.)

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).

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?