JEE Main 2019 · Mathematics · Probability · medium

A pair of unbiased dice is rolled once. If it is known that at least one die shows an even face, then the probability that the total of the two faces…

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A pair of unbiased dice is rolled once. If it is known that at least one die shows an even face, then the probability that the total of the two faces is 8 equals

A. $\frac{5}{36}$
B. $\frac{1}{12}$
C. $\frac{1}{9}$
D. $\frac{1}{3}$

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Answer: (C) $\frac{1}{9}$

Outcomes with at least one even number:

36-3\times3=27

. Among these, sum 8 occurs for

(2,6),(4,4),(6,2)

only, since

(3,5),(5,3)

have no even number. Probability

=\dfrac{3}{27}=\dfrac19

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