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JEE Main 2022 · Mathematics · Probability · medium

A pair of unbiased dice is rolled. Given that the first die shows an even face, the chance that the total is 8 equals

Single correct option

A pair of unbiased dice is rolled. Given that the first die shows an even face, the chance that the total is 88 equals
  1. A. 112\frac1{12}
  2. B. 16\frac16
  3. C. 118\frac1{18}
  4. D. 536\frac5{36}
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Answer: (B) 16\frac16

Given the first die is even there are 3×6=183\times6=18 equally likely outcomes. Favourable outcomes with sum 8 are (2,6),(4,4),(6,2)(2,6),(4,4),(6,2), i.e. 3. So the conditional probability is 318=16\frac3{18}=\frac16. Using the whole sample space gives 536\frac{5}{36}, which ignores the condition.
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Original question written in the JEE Main 2022 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake