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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Choose the correct answer from the given four options.
The probability distribution of a discrete random variable $X$ is given below:
$\text{X}$ $2$ $3$ $4$ $5$
$\text{P}(\text{X})$ $\frac{5}{\text{k}}$ $\frac{7}{\text{k}}$ $\frac{9}{\text{k}}$ $\frac{11}{\text{k}}$
The value of $k$ is:
  • A
    $8.$
  • B
    $16.$
  • ✓
    $32.$
  • D
    $48.$
✓

Answer

Correct option: C.
$32.$
We know that, $\sum\text{P}\text{X}=1$
$\Rightarrow\frac{5}{\text{k}}+\frac{7}{\text{k}}+\frac{9}{\text{k}}+\frac{11}{\text{k}}=1$
$\Rightarrow\frac{32}{\text{k}}=1$
$\therefore\text{k}=32$

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