Q251 / 270 · NDA 2018 (Phase 2) · Mathematics

If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is

  • A
    1/6
  • B
    4/11
  • Correct answer
    C
    3/11
  • D
    2/11

Solution

$\begin{aligned} & \mathrm{A}=\text { Event of showing } 5 \text { and atleast one dice } \\ & =(1,5),(2,5),(3,5),(4,5)(5,5),(6,5),(5,1) \text {, } \\ & (5,2),(5,3),(5,4),(5,6) \\ & n(\mathrm{~A})=11 \\ & \text { and } n(s)=6 \times 6=36 \\ & B=\text { Event of showing sum } 10 \text { or more when atleast one } \\ & \text { dice shows } 5 \\ & =(5,5),(5,6),(6,5) \\ & n(\mathrm{~B})=3 \\ & \Rightarrow \quad n(\mathrm{~A} \cap \mathrm{~B})=3 \\ & \text { Now, } \mathrm{P}\left(\frac{\mathrm{~B}}{\mathrm{~A}}\right)=\frac{\mathrm{P}(\mathrm{~A} \cap \mathrm{~B})}{\mathrm{P}(\mathrm{~A})} \\ & =\frac{\frac{n(\mathrm{~A} \cap \mathrm{~B})}{n(\mathrm{~S})}}{\frac{n(\mathrm{~A})}{n(\mathrm{~S})}}=\frac{\frac{3}{36}}{\frac{11}{36}}=\frac{3}{11} \end{aligned}$

Hence, the correct answer is option: 'C'.

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