Q59 / 150 · MHT CET 2024 (03 May Shift 1) · Mathematics

A random variable $x$ has the following probability distribution. Then value of $k$ is and $\mathrm{P}(3 \lt x \leq 6)$ has the value Figure

  • A
    $\frac{1}{20}, \frac{3}{7}$
  • B
    $\frac{5}{21}, \frac{3}{7}$
  • Correct answer
    C
    $\frac{1}{21}, \frac{3}{7}$
  • D
    $\frac{1}{20}, \frac{4}{7}$

Solution

$\begin{aligned} & \text {Since } \sum_{x=0}^8 \mathrm{P}(\mathrm{X}=x)=1 \\ & \therefore \quad \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+4 \mathrm{k}+4 \mathrm{k}+3 \mathrm{k}+2 \mathrm{k}+\mathrm{k}+\mathrm{k}=1 \\ & \Rightarrow \mathrm{k}=\frac{1}{21} \\ & \therefore \quad \mathrm{P}(3 \lt x \leq 6)=\mathrm{P}(\mathrm{X}=4)+\mathrm{P}(\mathrm{X}=5)+\mathrm{P}(\mathrm{X}=6) \\ &=\frac{4}{21}+\frac{3}{21}+\frac{2}{21} \\ &=\frac{9}{21}=\frac{3}{7}\end{aligned}$

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

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