CUET · MATHS · PYQ PAPER 2023
The probability that X can take the values \(x_i\) has the following form:
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.2 & \text { if } x_i=0 \\ k x_i & \text { if } x_i=1 \text { or } 2 \\ k\left(5-x_i\right) & \text { if } x_i=3 \\ 0 & \text { otherwise }\end{array}\right.\)
The value of P(X = 2) is:
- A \(\frac{4}{25}\)
- B \(\frac{3}{25}\)
- C \(\frac{6}{25}\)
- D \(\frac{8}{25}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{25}\)
Step-by-step Solution
Detailed explanation
\(\sum P(X=x_i) = 1\) \(0.2 + k(1) + k(2) + k(5-3) = 1\) \(0.2 + k + 2k + 2k = 1\) \(0.2 + 5k = 1\) \(5k = 0.8\) \(k = \frac{0.8}{5} = \frac{4}{25}\) \(P(X=2) = 2k\) \(P(X=2) = 2 \cdot \frac{4}{25} = \frac{8}{25}\)
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