JEE Mains · Maths · STD 12 - 13. probability
In a binomial distribution \(B ( n , p )\), the sum and product of the mean and variance are \(5\) and \(6\) respectively, then find \(6(n+p-q)\) is equal to :-
- A \(51\)
- B \(52\)
- C \(53\)
- D \(50\)
Answer & Solution
Correct Answer
(B) \(52\)
Step-by-step Solution
Detailed explanation
\(n p+n p q=5, n p \cdot n p q=6\) \(n p(1+q)=5, n^2 p^2 q=6\) \(n^2 p^2(1+q)^2=25, n^2 p^2 q=6\) \(\frac{6}{q}(1+q)^2=25\) \(6 q^2+12 q+6=25 q\) \(6 q^2-13 q+6=0\) \(6 q^2-9 q-4 q+6=0\) \((3 q-2)(2 q-3)=0\) \(q=\frac{2}{3}, \frac{3}{2}, q=\frac{2}{3} \text { is accepted }\)…
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