# Pe and f this leads to conditional probabilities pfe

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P(E and F) This leads to conditional probabilities: P(F|E) = ----------------------- P(E) P(drawing the first Ace) = 4/52 = 0.077 P(drawing a second Ace| first Ace) = 3/51 = 0.059 The probability of F occurring , given the occurrence of event E is P(F|E). Rearranging this equation gives us the general multiplication rule (for any events, independent or not): P(E and F) = P(E) • P(F|E) The probability of E and F occurring is P(E) occurring times P(F|E) (probability of F occurring given that E has occurred. If E and F are independent then P(F|E) = P(F). Note : in our problems we will be given all but one of the probabilities and then have to use the equations to find the missing probability. Sampling Rule of Thumb : with small random samples are taken from a large population without replacements, if sample size is less than 5% of the population size, we can treat events as independent. Multiplication Rule of Counting : p•q•r• …. For p choices of item 1, q choices of item 2, r choices of item 3 and so on. Permutations : order is important! Combinations : order is not important n! means (n) • (n-1) • (n-2) • (n-3) • … • 2 • 1 (read n factorial) Calculator can calculate factorials, permutations and combinations using math key and PRB option. Instructions on pg 306 of out text book.
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