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Section 7.4 Use of Counting Techniques in Probability Computing the Probability of an Event in a Uniform Sample Space Let S be a uniform sample space and let E be any event. Then number of favorable outcomes in E n E PE number of possible outcomes in S nS Ex. Suppose that you reach into a box of 12 size AA batteries and you know that 4 of them are dead. Find the probability that a. in one draw you get a good battery. n good batteries n batteries C 8,1 C 12,1 8 2 12 3 b. in two draws without replacement you get two good batteries. n ways to get 2 good n ways to draw 2 batteries C 8, 2 C 12, 2 28 14 66 33 Ex. Three balls are selected at random without replacement from the jar below. Find the probability that a. All 3 of the balls are green. n draw 3 green n draw 3 C 3,3 C 8,3 1 56 b. One ball is red and two are black. n draw 1 red, 2 black n draw 3 C 2,1 C 3, 2 C 8,3 6 3 56 28 Ex. Refer to the jar of marbles below. Two marbles are drawn at random without replacement. Find the probability that no yellow are drawn. 1 P both yellow 1 C 3, 2 C 11, 2 3 52 1 55 55