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AIEEE 2003

JEE Main 2003 Mathematics question on Probability

Two numbers are selected randomly from the set S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\} without replacement one by one. The probability that minimum of the two numbers is less than 4, is
  1. A.
    1/15
  2. B.
    14/15
  3. C.
    1/5
  4. D.
    4/5
Show answer and solution

Correct option: D

Solution

The complement is that the minimum of the two numbers is ≥ 4, meaning both numbers are from {4, 5, 6}. The number of ways to choose 2 from {4, 5, 6} is C(3,2) = 3, and total ways to choose 2 from 6 is C(6,2) = 15. So P(min ≥ 4) = 3/15 = 1/5, and P(min < 4) = 1 - 1/5 = 4/5.

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