JEE Mains · Maths · STD 11 - 13. statistics
From a lot of \(12\) items containing \(3\) defectives, a sample of \(5\) items is drawn at random. Let the random variable \(\mathrm{X}\) denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of \(X\) is \(\frac{m}{n}\), where \(\operatorname{gcd}(m, n)=1\), then \(n-m\) is equal to ...........
- A \(71\)
- B \(34\)
- C \(72\)
- D \(76\)
Answer & Solution
Correct Answer
(A) \(71\)
Step-by-step Solution
Detailed explanation
\( \mathrm{a}=1-\frac{{ }^3 \mathrm{C}_5}{{ }^{12} \mathrm{C}_5} \) \( \mathrm{~b}=3 \cdot \frac{{ }^9 \mathrm{C}_4}{{ }^{12} \mathrm{C}_5} \) \( \mathrm{c}=3 \cdot \frac{{ }^9 \mathrm{C}_3}{{ }^{12} \mathrm{C}_5} \)…
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