A box contains 9 green and 7 yellow balls. Two balls are drawn in succession at random. What is the probability that one of them is green and the other is yellow?
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There are two ways to get one green and one yellow ball: green first, then yellow, or yellow first then green. There are 9+7=16 total balls, so, if the first ball picked is removed from the group of balls from which the next ball is picked, then the probability of green then yellow is (9/16)×(7/15) while the probability of yellow then green is (7/16)×(9/15). We need to add these together: (9/16)×(7/15) + (7/16)×(9/15) = 63/240 + 63/240 = 126/240 = 63/120 = 21/40
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