JEE Main 2021 (Online) 27th August Evening ShiftQuestion 1
The probability distribution of random variable $X$ is given by :
$X$ : $1,2,3,4,5$
$P(X)$ : $K,2K,2K,3K,K$
Let $p=P(1<X<4\mid X<3)$. If $5p=\lambda K$, then $\lambda$ is equal to $\_\_\_\_\_\_$ .
Probability
Answer$30$
Solution
$9K=1\Rightarrow K=\frac19$. $p=\frac{P(X=2)}{P(X<3)}=\frac{2K}{3K}=\frac23$. $5p=\frac{10}3=\lambda K=\frac\lambda9\Rightarrow\lambda=30$.