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Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6) and let $E_{k} = {(a, b) \in S : a b = k}$ for $k \geq 1$ . If $P_{k} = P (E_{k})$ for $k \geq 1$ for then the correct, among the following is

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$P_{1} < P_{30} < P_{4} < P_{6}$

$P_{36} < P_{6} < P_{2} < P_{4}$

$P_{1} < P_{11} < P_{4} < P_{6}$

$P_{36} < P_{11} < P_{6} < P_{4}$

answer is A.

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Detailed Solution

$P_{1} = \frac{1}{36}, P_{30} = \frac{2}{36}$

$P_{4} = \frac{3}{36}, P_{6} = \frac{4}{36}$

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