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  • Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that  &nbsp

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that  2N<N!   is \frac{m}{n} , 

Option: 1

12


Option: 2

8


Option: 3

10


Option: 4

6


Answers (1)

best_answer

2N<N!   is satisfied for N > 4
Required probability \mathrm{P}(\mathrm{N} \geq 4)=1-\mathrm{P}(\mathrm{N}<4)
N = 1 (Not possible)
N = 2 (1, 1) 

\begin{aligned} & \Rightarrow \mathrm{P}(\mathrm{N}=2)=\frac{1}{36} \\ & \mathrm{~N}=3(1,2),(2,1) \\ & \Rightarrow \mathrm{P}(\mathrm{N}=3)=\frac{2}{36} \\ & \mathrm{P}(\mathrm{N}<4)=\frac{1}{36}+\frac{2}{36}=\frac{3}{36} \\ & \therefore \mathrm{P}(\mathrm{N} \geq 4)=1-\frac{3}{36}=\frac{33}{36}=\frac{11}{12}=\frac{\mathrm{m}}{\mathrm{n}} \\ \end{aligned}

\begin{aligned} & \Rightarrow \mathrm{m}=11, \mathrm{n}=12 \\ & \therefore 4 \mathrm{~m}-3 \mathrm{n}=4(11)-3(12)=8 \end{aligned}

 

Posted by

HARSH KANKARIA

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