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Probability of drawing yellow and black balls

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Probability

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In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?

  1. A.

    1/16

  2. B.

    28/55

  3. C.

    3/8

  4. D.

    8C2 / 4C1

Answer

B

Explanation

Total balls = 8+4=128 + 4 = 12. Total ways to choose 3 balls = (123)=12×11×106=220\binom{12}{3} = \frac{12 \times 11 \times 10}{6} = 220. Favorable ways = (82)×(41)=28×4=112\binom{8}{2} \times \binom{4}{1} = 28 \times 4 = 112. Probability = 112220=2855\frac{112}{220} = \frac{28}{55}.

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