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Previous Year Question (PYQs)

A black and a red die are rolled together. What is the conditional probability of obtaining the sum $8$, given that the red die resulted in a number less than $4$?




Solution

Condition: red die ∈ {1,2,3} → sample size $3 \times 6 = 18$ equiprobable outcomes. Sum $8$ occurs with $(r,b)=(2,6),(3,5)$ → 2 favorable outcomes. $P(\text{sum }8 \mid r<4) = \dfrac{2}{18} = \dfrac{1}{9}$. $\boxed{\text{Answer: (C) } \tfrac{1}{9}}$

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