JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Probability

In a binomial distribution

B (n, p)

, the sum and product of the mean & variance are 5 and 6 respectively, then find

6 (n + p - q)

is equal to :-

Answer: (B)

Solution

With mean

n p

and variance

n pq

, the data give

n p (1 + q) = 5

and

(n p) (n pq) = 6

. Squaring the first and dividing by the second,

\frac{( 1 + q ) ^{2}}{q} = \frac{25}{6}

, i.e.

6 q^{2} - 13 q + 6 = 0

, whose admissible root is

q = \frac{2}{3}

, so

p = \frac{1}{3}

. Then

n p \cdot \frac{5}{3} = 5

gives

n p = 3

and

n = 9

. Therefore

6 (n + p - q) = 6 (9 + \frac{1}{3} - \frac{2}{3}) = 6 \cdot \frac{26}{3} = 52

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option