List of top Mathematics Questions on Probability asked in AP PGECET

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A}) = 0.3$, $P(B) = 0.4$ and $P(A \cap \bar{B}) = 0.5$, then $P(A \cup B) = \_\_\_\_\_\_\_$
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 ...........
In a binomial distribution \( B(n = 10, p) \), the probability of getting exactly 4 successes equals the probability of getting exactly 6 successes. What is the mean of the distribution?
If \( A \) and \( B \) are two events having probabilities, \( P(A) = 0.6 \), \( P(B) = 0.3 \), and \( P(A \cap B) = 0.2 \), then the probability that neither \( A \) nor \( B \) occurs is ______

The probability distribution of a random variable \( X \) is given as follows. Then, \( P(X = 50) - \frac{P(X \leq 30)}{P(X \geq 20)} \) = 

The probability distribution of a random variable \( X \) is given below:
\[ \begin{array}{|c|c|c|c|c|c|} \hline X = x & 10 & 20 & 30 & 40 & 50 \\ \hline P(X = x) & k & 2k & 3k & 4k & 5k \\ \hline \end{array} \] Then, \( P(X = 50) - \dfrac{P(X < 30)}{P(X > 20)} \) = ...........
If \( X \) is a continuous random variable with the probability density function \[ f(x) = \begin{cases} K(1 - x^3), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases} \] Then, the value of \( K \) is ..........