JEE Mains · Maths · STD 12 - 13. probability
A bag contains \(4\) white and \(6\) black balls. Three balls are drawn at random from the bag. Let \(X\) be the number of white balls, among the drawn balls. If \(\sigma^{2}\) is the variance of \(X\), then \(100 \sigma^{2}\) is equal to.
- A \(55\)
- B \(54\)
- C \(56\)
- D \(53\)
Answer & Solution
Correct Answer
(C) \(56\)
Step-by-step Solution
Detailed explanation
\(X\) \(0\) \(1\) \(2\) \(3\) \(P(X)\) \(\frac{1}{6}\) \(\frac{1}{2}\) \(\frac{3}{10}\) \(\frac{1}{30}\) \(\sigma^{2}=\sum X ^{2} P ( X )-\left(\sum XP ( X )\right)^{2}=\frac{56}{100}\) \(100 \sigma^{2}=56\)
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