Probability Questions

Let $X$ be a discrete random variable with probability $P(X=x)=\frac{1}{2^x}$ for $x=1,2,3,\dots$. Then the expected value of $X$ is:

Consider the probability distribution function defined as $f_X(x)=\{\begin{array}{ll}|x|,& |x|<1\\ 0,& \text{otherwise}\end{array}$. Which of the following is true?

Find the number of ways of picking $4$ cards from a set of $52$ playing cards if all four cards are of the same suit?

Urn A consists of $3$ blue and $4$ green balls while another urn B consists of $5$ blue and $6$ green balls. One ball is drawn at random from one of the urns and it is found to be blue. Determine the probability that it was drawn from urn B?

Which of the following is true for binomial distribution?

If $X$ and $Y$ are random variables such that $E(X)=10$, $V(X)=25$ and $E(Y)=0$, $V(Y)=1$, the values of $a,b$ such that $Y=aX-b$ will be:

In a job placement event, there are $1000$ aspirants attending a company interview, out of which $430$ are females. It is known that $10\%$ of the females are graduates. Determine the probability that an aspirant selected randomly is a graduate given that the selected aspirant is a female?