Probability of Note Values

XAT 2022 · Quantitative Ability & Data Interpretation · Easy · Probability

I have five 10-rupee notes, three 20-rupee notes, and two 50-rupee notes in my wallet. If three notes were taken out randomly and simultaneously, what is the probability that at least 90 rupees were taken out?

  1. A.

    1/20

  2. B.

    7/60

  3. C.

    1/15

  4. D.

    11/60

  5. E.

    3/20

Answer

B

Explanation

Total ways to choose 3 notes out of 10 =(103)=120= \binom{10}{3} = 120. To get sum ≥90\ge 90:

  • Two Rs 50 + One Rs 20: (22)×(31)=3\binom{2}{2} \times \binom{3}{1} = 3
  • Two Rs 50 + One Rs 10: (22)×(51)=5\binom{2}{2} \times \binom{5}{1} = 5
  • One Rs 50 + Two Rs 20: (21)×(32)=6\binom{2}{1} \times \binom{3}{2} = 6 Total favorable outcomes = 3+5+6=143 + 5 + 6 = 14. Probability = 14/120=7/6014 / 120 = 7 / 60.

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