WBJEE · Maths · Probability
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 :
- A \(p_1 < p_{10} < p_4\)
- B \(\mathrm{p}_2 < \mathrm{p}_8 < \mathrm{p}_{14}\)
- C \(\mathrm{p}_4 < \mathrm{p}_8 < \mathrm{p}_{17}\)
- D \(\mathrm{p}_2 < \mathrm{p}_{16} < \mathrm{p}_5\)
Answer & Solution
Correct Answer
(A) \(p_1 < p_{10} < p_4\)
Step-by-step Solution
Detailed explanation
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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