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JEE Main 2024 · Mathematics · Probability · medium

Given that the first die shows an odd number, the probability that the sum is 7 is

Single correct option

Two fair dice are thrown. Given that the first die shows an odd number, the probability that the sum is 77 is
  1. A. 112\dfrac{1}{12}
  2. B. 13\dfrac{1}{3}
  3. C. 14\dfrac{1}{4}
  4. D. 16\dfrac16
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Answer: (D) 16\dfrac16

The conditioning event has 3×6=183\times6=18 outcomes. Sum 77 with an odd first die: (1,6),(3,4),(5,2)(1,6),(3,4),(5,2), i.e. 33 outcomes. So P=318=16P=\dfrac{3}{18}=\dfrac16. Note the unconditional probability of sum 77 is also 16\tfrac16.
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Original question written in the JEE Main 2024 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake