If probability function of a discrete random variable $X$ is $P(X=r)=r / k, r=1,2,3,4,5$, then $P\left(X=2\right.$ or $\left.X=\frac{k}{3}\right)$, is

• A

  $P(X=1$ or $X=6)$
• Correct answer
  B

  $P\left(X=4\right.$ or $\left.X=\frac{k}{5}\right)$
• C

  $P\left(x=\frac{k}{5}\right.$ or $\left.x=5\right)$
• D

  $P\left(x=\frac{k}{3}\right.$ or $\left.x=0\right)$

Solution

$P(X=r)=r / k$
$\begin{aligned} P\left(X_i\right)=1 \Rightarrow \frac{1+2+3+4+5}{k}=1 \Rightarrow k=15 & \left.=\frac{k}{3}\right)=P(x=2)+P\left(X=\frac{15}{3}\right) \\ P\left(X=2 \text { or } X=\frac{2}{15}+\frac{5}{15}=\frac{7}{15}\right. & =P(X=4)+P\left(X=\frac{15}{5}\right) \\ P\left(X=4 \text { or } X=\frac{k}{5}\right) & =P\left(\frac{4}{15}+\frac{3}{15}=\frac{7}{15}\right.\end{aligned}$

Hence, the correct answer is option: 'B'.