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AP EAMCET · Maths · Probability

If \(\mathrm{X}\) is random variable with probability distribution \(P(X=k)=\frac{(k+1) c}{2^k}, k=0,1,2, \ldots\), then \(P(X \geq 3)=\)

  1. A \(\frac{1}{4}\)
  2. B \(\frac{5}{16}\)
  3. C \(\frac{5}{11}\)
  4. D \(\frac{3}{16}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{5}{16}\)

Step-by-step Solution

Detailed explanation

\text { } \begin{gathered} \because P(X=k)=\frac{(k+1) C}{2^k}, k=0,1,2, \ldots . \\ \sum P(X=\mathrm{k})=\mathrm{C}\left(1+\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+\ldots\right) \\ \Rightarrow 1=C\left(1+\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+\ldots\right) \\ \Rightarrow…