JEE Main 2021 (25 Jul, Shift 2) Maths Q70: Probability

Question

Let X be a random variable such that the probability function of a distribution is given by
$P(X=0)=\frac{1}{2}$, $P(X=j)=\frac{1}{3^j}$ $(j=1,2,3,.....,\infty)$ Then the mean of the distribution and
P(X is positive and even) respectively are :

Accepted Answer

Option 1: $\frac{3}{4}$ and $\frac{1}{8}$

Answer

$\frac{3}{4}$ and $\frac{1}{8}$

Answer

$\frac{3}{4}$ and $\frac{1}{16}$

Answer

$\frac{3}{8}$ and $\frac{1}{8}$

Answer

$\frac{3}{4}$ and $\frac{1}{9}$

JEE Main 25 July 2021, Shift 2, Maths Q70

Same idea in other shifts