A) \[{{p}_{1}}={{p}_{2}}\]
B) \[{{p}_{1}}<{{p}_{2}}\]
C) \[{{p}_{1}}>{{p}_{2}}\]
D) None of these
Correct Answer: C
Solution :
\[{{p}_{1}}=\frac{6}{36}=\frac{1}{6}\] To find \[{{p}_{2}},\] the total number of ways \[={{6}^{4}}\]and since two numbers out of 6 can be selected in \[{}^{6}{{C}_{2}}\] ways i.e. 15 ways and corresponding to each of these ways, there are 8 ways e.g., \[(1,\,\,1,\,\,1,\,\,2)\,\,(1,\,\,1,\,\,2,\,\,1)\,.....\] Thus favourable ways \[=15\times 8=120\] Hence \[{{p}_{2}}=\frac{120}{{{6}^{4}}}=\frac{5}{54}\]. Hence \[{{p}_{1}}>{{p}_{2}}.\]
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