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JEE Main 2019 · 10 Apr · Shift I

JEE Main 2019 Mathematics question on Probability

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls; is
  1. A.
    117\dfrac{1}{17}
  2. B.
    112\dfrac{1}{12}
  3. C.
    110\dfrac{1}{10}
  4. D.
    111\dfrac{1}{11}
Show answer and solution

Correct option: D

Solution

Total children across two families = 4, each equally likely boy/girl, so 2⁴ = 16 equally likely outcomes.

Event A: all 4 are girls → 1 way → P(A) = 1/16.

Event B: at least 2 are girls → total outcomes minus (0 girls: 1 way) minus (exactly 1 girl: C(4,1)=4 ways) = 16 - 1 - 4 = 11 ways → P(B) = 11/16.

Conditional probability = P(A∩B)/P(B) = (1/16)/(11/16) = 1/11.

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