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
$( Sum = 4 ) \equiv{(1,3),(3,1),(2,2)}$
$n(A)=3$
$P(A)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48} \Rightarrow k=4$
