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Study the given information carefully and answer the questions that follow:
An urn contains 3 red, 6 blue, 2 green and 4 yellow marbles.If four marbles are picked at random, what is the probability that at least one is yellow ?
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By: anil on 05 May 2019 01.39 am
Total number of marbles in the urn = 15 P(S) = Total possible outcomes = Selecting 4 marbles at random out of 15 => $$P(S) = ^{15}C_4 = frac{15 imes 14 imes 13 imes 12}{1 imes 2 imes 3 imes 4}$$ = $$1365$$ Let no yellow marble is selected. P(E) = Favorable outcomes = Selecting 4 out of 11 marbles. => $$P(E) = ^{11}C_4$$ = $$frac{11 imes 10 imes 9 imes 8}{1 imes 2 imes 3 imes 4}$$ = $$330$$ $$ herefore$$ Required probability = $$1 - frac{P(E)}{P(S)}$$ = $$1 - frac{330}{1365} = 1 - frac{22}{91}$$ = $$frac{91 - 22}{91} = frac{69}{91}$$
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