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Marbles Drawing Probability

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Probability

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Aditya has a total of 18 red and blue marbles in two bags (each bag has marbles of both colors). A marble is randomly drawn from the first bag followed by another randomly drawn from the second bag, the probability of both being red is 5/16. What is the probability of both marbles being blue?

  1. A.

    1/16

  2. B.

    2/16

  3. C.

    3/16

  4. D.

    4/16

  5. E.

    5/16

Answer

C

Explanation

Let P(R1)=5/8P(R_1) = 5/8 and P(R2)=1/2P(R_2) = 1/2 so P(R1)P(R2)=5/16P(R_1) P(R_2) = 5/16. P(B1)=1−5/8=3/8P(B_1) = 1 - 5/8 = 3/8 and P(B2)=1−1/2=1/2P(B_2) = 1 - 1/2 = 1/2. P(both blue)=P(B1)P(B2)=38×12=316P(\text{both blue}) = P(B_1) P(B_2) = \frac{3}{8} \times \frac{1}{2} = \frac{3}{16}.

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