JEE Mains · Maths · STD 11 - 13. statistics
Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, \( x>y \) be 8 and 16 respectively. Two numbers are chosen from {1, 2, 3, x-4, y, 5} one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is:
- A \(\frac{3}{5}\)
- B \(\frac{4}{5}\)
- C \(\frac{2}{5}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{4}{5}\)
Step-by-step Solution
Detailed explanation
Mean \( (\overline{x})=8\) (Given) \(\Rightarrow \frac{2+4+10+x+12+14+y}{7}=8\) \(\Rightarrow x+y=14 \) ....(1) Variance \((\sigma^{2})=16\) (Given) \(\Rightarrow 16=\frac{2^{2}+4^{2}+10^{2}+x^{2}+12^{2}+14^{2}+y^{2}}{7}-8^{2}\) \(\Rightarrow x^{2}+y^{2}=100 \) ....(2)…
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