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Probability Ratio of Playing Cards

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Probability

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Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one of the cards drawn is a king, and b denote the probability of not drawing a king. The ratio a/b is

  1. A.

    ≥0.25 and <0.5\ge 0.25 \text{ and } < 0.5

  2. B.

    ≥0.5 and <0.75\ge 0.5 \text{ and } < 0.75

  3. C.

    ≥0.75 and <1.0\ge 0.75 \text{ and } < 1.0

  4. D.

    ≥1.0 and <1.25\ge 1.0 \text{ and } < 1.25

  5. E.

    ≥1.25\ge 1.25

Answer

E

Explanation

Total ways to choose 2 cards from 6 = (62)=15\binom{6}{2} = 15. Ways to draw NO kings (both non-kings from 4 non-kings) = (42)=6\binom{4}{2} = 6. Probability b=6/15=2/5b = 6/15 = 2/5. Probability a=1−b=9/15=3/5a = 1 - b = 9/15 = 3/5. Ratio a/b=(9/15)/(6/15)=9/6=1.5a/b = (9/15) / (6/15) = 9/6 = 1.5. Since 1.5≥1.251.5 \ge 1.25, option E is correct.

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