TS EAMCET · Maths · Probability
The range of a discrete random variable X is \(\{1,2,3\}\) and the probabilities of its elements are given by \(\mathrm{P}(\mathrm{X}=1)=3 \mathrm{k}^3, \mathrm{P}(\mathrm{X}=2)=2 \mathrm{k}^2\) and \(\mathrm{P}(\mathrm{X}=3)=7-19 \mathrm{k}\). Then \(\mathrm{P}(\mathrm{X}=3)=\)
- A \(\frac{2}{3}\)
- B \(\frac{2}{9}\)
- C \(\frac{1}{9}\)
- D \(\frac{4}{9}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\(P(X=1)+P(X=2)+P(X=3)=1\) \(3k^3+2k^2+(7-19k)=1\) \(3k^3+2k^2-19k+6=0\) \(k=\frac{1}{3}\) \(P(X=3)=7-19k\) \(P(X=3)=7-19\left(\frac{1}{3}\right)\) \(P(X=3)=\frac{21-19}{3}\) \(P(X=3)=\frac{2}{3}\)
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