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AP Statistics Section 6.2 B Probability Rules If A represents some event, then the probability of event a happening can be represented as _____ P (A) Probability Rules 1. A probability must be a number between 0 and 1 inclusive. Thus, 0 P(A) 1 for any event A, ____________ 2. The sum of the probabilities of all possible outcomes of some “procedure” must equal ___. 1 If S is the sample space in a probability model, then P(S) = ____. 1 3. Two events are disjoint (also called mutually exclusive) if they have no outcomes in common (i.e. the events can never occur simultaneously). For example, rolling a pair of dice and getting a sum of seven and rolling a pair of dice and getting doubles would be mutually exclusive events. If A and B are disjoint, then P(A or B) = P(A) __________. P(B) This is the addition rule for disjoint events. In place of “or” we may also use the symbol for a “union” _____. Similarly, we may use the intersection symbol ______ instead for the “empty of “and” and ___ event” (i.e. the event with no outcomes in it) _________________________ If two events A and B are disjoint we can write ___________ AB The probability that an event does not occur is 1-probability the event does occur. For an event A, the event that A does not occur is called the c A complement of A, written _____ The complement rule states that: c P(A ) 1 P( A) _______________. Disjoint and complement are important terms for us to understand. Perhaps we can use Venn diagrams to clarify. In each case the large rectangle represents our sample space. Disjoint and complement are important terms for us to understand. Perhaps we can use Venn diagrams to clarify. In each case the large rectangle represents our sample space. A A c Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year. Note that each probability is between 0 and 1, and that the sum of the probabilities is 1 because these 4 outcomes make up the sample space. Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year. Find: P(WS lasts 5 games) .2121 Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year. Find: P(WS does not last 5 games) 1 .2121 .7879 Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year. Find: P(WS lasts 6 or 7 games) .2323 .3737 .6060 Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year. Find: P(WS lasts 8 games) 0 In the special situation where all outcomes are equally likely, we have a simple rule for assigning probabilities to events. If a random phenomenon has k possible outcomes that are all equally likely, then the probability of each 1 individual outcome is _____. k The probability of an event A is number of outcomes in A P(A) = k