Question

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

• A. 16
• B. 2
• C. 8
• D. 4

Answer 1

Answer: (D)

$n(s)=36$
Given : $N-2,\sqrt{3N},N+2$ are in G.P.
$3N=(N-2)(N+2)$
$3N=N^2-4$
$\Rightarrow N^2-3N-4=0$
$(N-4)(N+1)=0\Rightarrow N=4\text{ or }N=-1\text{ rejected }$
$(Sum=4)\equiv \{(1,3),(3,1),(2,2)\}$
$n(A)=3$
$P(A)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48}\Rightarrow k=4$