Let N be the sum of the numbers appeared when two fair dice are rolled and let the probabi…

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 :

Accepted Answer

$n-2, \sqrt{3 n}, n+2 ightarrow$ G.P.

$3 n=n^{2}-4$

$\Rightarrow n^{2}-3 n-4=0$

$\Rightarrow n=4,-1$ (rejected)

$P(S=4)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48}$

$	herefore k=4$

Solutions · 1