Question
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Answer: Option C
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Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that both marbles are blue = ³Câ‚‚/¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35 Probability that both are yellow = ²Câ‚‚/¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105 Probability that one blue and other is yellow = (³Câ‚ * ²Câ‚)/¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35 Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 * 35) = 2/21
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