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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
The probability distribution of a random variable $X$ is:
X  01234
P(X)    0.1                      k                    2k                      k0.1
where $k$ is some unknown constant.
The probability that the random variable $X$ takes the value 2 is:
  • A
    $\frac{1}{5}$
  • B
    $\frac{2}{5}$
  • C
    $\frac{4}{5}$
  • D
    1
✓

Answer

$\begin{array}{l}\text {As } \sum_{i=1}^n p_i=1 \Rightarrow 0.1+k+2 k+k+0.1=1 \\ \Rightarrow \quad 4 k=1-0.2=0.8 \Rightarrow k=\frac{0.8}{4}=0.2 \\ \therefore \quad P(x=2)=2 k=2 \times 0.2=0.4=\frac{4}{10}=\frac{2}{5}\end{array}$

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