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Probability

Let S be th...

Question

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 $E_{K} = {(a, b) ϵ S : a b = K}$ for $K \geq 1$ if $P_{k} = P (E_{k}) f o r k \geq 1$ , then correct relation among the following is

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

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

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

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

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Solution

The correct option is B $P_{1} < P_{30} < P_{4} < P_{6}$
The Sample Space will be
$S :$
$= (1, 1), (1, 2) . . . (1, 6)$
$(2, 1) . . . (2, 6)$
:
:
:
$(6, 1) . . . (6, 6)$
Hence the total number of elements in the sample space is $6^{2}$
$= 36$
$p (1, 1) = \frac{1}{36}$
Hence answer is option A.

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