JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q17

MathematicsSingle correct+4 / -1Question 17 of 90

Let X be a random variable having binomial distribution $B(7,p)$ . If $P(X=3)=5P(X=4)$ , then the sum of the mean and the variance of X is :

\dfrac{105}{16}

\dfrac7{16}

\dfrac{77}{36}

\dfrac{49}{16}

Answer and worked solution

Official answer: C

Find p. $\binom73p^3q^4=5\binom74p^4q^3$ gives $q=5p$ , so $p=\frac16$ .

Mean and variance. $\frac76+\frac{35}{36}=\frac{77}{36}$ .

(C)

Topics:Binomial distribution

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 17