Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 & 3. If X denotes the sum of the numbers, then the expected value of X is...

Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white ball is...

Let $a$ be an integer selected at random from the set $\{0, 1, 2, 3, \ldots, 9\}$. The probability that the equation $ax^2 - ax + 1 = 0$ has real roots is ...

If in $6$ trials, X is a binomial random variable which follows the relation $9P(x = 4) = P(x = 2)$, then the probability of failure is...