9.1 Understanding Probability Remember to Silence Your Cell Phone and Put It In Your Bag! Defining Probability The use of numbers to describe the chance that something will happen. The ratio of favorable occurrences to the number of total possible occurrences of an observable event. For this class, unless asked to do differently, write your probabilities as simplified fractions Terminology Experiment Outcome Sample Space Equally Likely Uniform Sample Space Nonuniform Sample Space Event Example Uniform Sample Space Example Nonuniform Sample Space Defining Probability (cont.) Probability, P, of an event A for a uniform sample space: P( A ) Number of outcomes associated with the event A Number of outcomes in the sample space S Probability, P, of an event A for a nonuniform sample space: P( A ) Measure of the outcomes associated with the event A Measure of all of the outcomes in the sample space S Terminology (cont.) Random Event Certain Event Impossible Event Complementary Events Mutually Exclusive Events Non-mutually Exclusive Events Properties of Probability 1. 0 P(A) 1 2. The sum of the probabilities of all outcomes in the sample space is 1 3. P(a certain event) = 1 4. P(an impossible event) = 0 5. If A and B are complementary events, P(A) = 1 – P(B) Properties of Probability (cont.) 6. If A and B are mutually exclusive events, P(A or B) = P(A) + P(B) 7. If A and B are non-mutually exclusive events, P(A or B) = P(A) + P(B) – P(A and B) Law of Large Numbers Empirical Probability Theoretical Probability Law of Large Numbers If an experiment is repeated many times, the empirical probability of an event will approach the theoretical probability of the event occurring.