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 :
Solution
$n-2, \sqrt{3 n}, n+2 \rightarrow$ G.P.
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$3 n=n^{2}-4$
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$\Rightarrow n^{2}-3 n-4=0$
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$\Rightarrow n=4,-1$ (rejected)
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$P(S=4)=\frac{3}{36}=\frac{1}{12}=\frac{4}{48}$
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$\therefore k=4$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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