Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k=\{a, b) \in$ $S: a b=k\}$. If $p_k=P\left(E_k\right)$, then the correct among the following is :

Question

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k=\{a, b) \in$ $S: a b=k\}$. If $p_k=P\left(E_k\right)$, then the correct among the following is :, $p_1 < p_{10} < p_4$, $\mathrm{p}_2 < \mathrm{p}_8 < \mathrm{p}_{14}$, $\mathrm{p}_4 < \mathrm{p}_8 < \mathrm{p}_{17}$, $\mathrm{p}_2 < \mathrm{p}_{16} < \mathrm{p}_5$

MARKS App · Accepted Answer

Hint: $E_1=\{(1,1)\}, \quad E_4=\{(2,2),(1,4),(4,1)\} \quad E_{10}=\{(2,5),(5,2)\}$ $p_1=\frac{1}{36}$ $p_4=\frac{3}{36}=\frac{1}{12}$, $p_{10}=\frac{2}{36}=\frac{1}{18}$

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