P(E and F)This leads to conditional probabilities: P(F|E) = -----------------------P(E)P(drawing the first Ace) = 4/52 = 0.077P(drawing a second Ace| first Ace) = 3/51 = 0.059The 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 independentthen 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 importantn! 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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