### Probability Question 5

#### Question 5 - 25 January - Shift 2

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2, \sqrt{3 N}, N+2$ are in geometric progression be $\frac{k}{48}$. Then the value of $k$ is

(1) 2

(2) 4

(3) 16

(4) 8

## Show Answer

#### Answer: (2)

#### Solution:

#### Formula: Geometric Progression, Roots of equations, Probability of occurrence of an event

$ n(s)=36 $

Given : $N-2, \sqrt{3 N}, N+2$ are in G.P.

$ \begin{aligned} & 3 N=(N-2)(N+2) \\ & 3 N=N^{2}-4 \\ & \Rightarrow N^{2}-3 N-4=0 \end{aligned} $

$(N-4)(N+1)=0 \Rightarrow N=4$ or $N=-1$ rejected

$( Sum = 4 ) \equiv{(1,3),(3,1),(2,2)}$

$n(A)=3$

$P(A)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48} \Rightarrow k=4$