Consider a game of tossing a six sided fair die. If the face that comes up is $6$, the player wins Rs. $36$ and he loses Rs. $k^2$, where $k$ is the face that comes up $k = \{1, 2, 3, 4, 5\}$, then the expected winning amount in this game in Rs. is...

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is $\ldots$

If the p. d. f. of a continuous random variable X is given by $f(x) = \begin{cases} k(9 + 8x - x^2), & \text{for } -1 \leq x \leq 4 \\ 0, & \text{otherwise} \end{cases}$ then the value of $k$ is $\ldots$

In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing is