In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.

The p.m.f of a random variable $X$ is $P(X=x)=\frac{1}{2^5}\binom{5}{x}$,where $x=0, 1, 2, 3, 4, 5$ and $P(X=x)=0$ otherwise. Then:

If two cards are drawn randomly from a pack of $52$ playing cards,then the mean of the probability distribution of the number of kings is

If the probability function of a discrete random variable $X$ is $P(X=r) = r/k$ for $r = 1, 2, 3, 4, 5$, then $P(X=2 \text{ or } X=k/3)$ is equal to:

If on an average $4$ customers visit a shop in an hour, then the probability that more than $2$ customers visit the shop in a specific hour is

If a drunkard person tries to take a step,then it will be a forward or backward step with probabilities $\frac{1}{4}$ and $\frac{1}{2}$ respectively,or he will remain in his 'as it is' position. If he tries to take a step $5$ times,then find the probability that he will be one step away from the initial position.