List of top Mathematics Questions on Probability and Statistics asked in AP PGECET

A number is selected randomly from each of the following two sets:
{1, 2, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8, 9}
What is the probability that the sum of the numbers is 9?

Let $X$ be an exponential random variable with mean parameter one. Then the conditional probability $P(X>10 | X>5)$ is equal to

The number of accidents occurring in AU region in a month follows Poisson distribution with mean $\lambda = 5$. The probability of less than two accidents in a randomly selected month is ______

If \( X \) is a continuous random variable with the probability density
\[ f(x) = \begin{cases} K(1 - x^3), & 0 < x < 1 \\ 0, & \text{otherwise} \end{cases} \] Then, the value of \( K \) is ............

The probability of a component being defective is 0.01. There are 100 such components in a machine. Then the probability of two or more defective components in the machine is _______

If \( A \) and \( B \) are two mutually exclusive events with \( P(B) \ne 1 \), then the conditional probability \[ P(A \mid \overline{B}) = \,? \] where \( \overline{B} \) is the complement of \( B \)

If \( X \) is a continuous random variable with the probability density function
\[ f(x) = \begin{cases} cx^3, & 0 \le x \le 2 \\ 0, & \text{otherwise} \end{cases} \] then \( P\left( \frac{1}{2} < X < \frac{3}{2} \right) \) is ..........