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

If a unit vector is represented by $\vec{U} = 0.9\,\hat{i} - 0.2\,\hat{j} + m\hat{k}$, then the value of m is