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AP EAMCET · Maths · Probability

If the probability function of a random variable \(X\) is defined by \(P(X=k)=a\left(\frac{k+1}{2^k}\right)\) for \(k=0,1,2,3,4,5\), then the probability that \(X\) takes a prime value is

  1. A \(\frac{13}{20}\)
  2. B \(\frac{23}{60}\)
  3. C \(\frac{11}{20}\)
  4. D \(\frac{19}{60}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{23}{60}\)

Step-by-step Solution

Detailed explanation

We have, \[ P(x=k)=a\left(\frac{k+1}{2^k}\right) \] We know that, \[ \begin{gathered} \Sigma P(x=k)=1 \\ \Rightarrow \quad P(x=0)+P(x=1) \\ +P(x=2)+P(x=3)+P(x=4)+P(x=5)=1 \end{gathered} \]…