Two dice are rolled. Then,the probability that the total score is a prime number is

Two dice are thrown together. If the numbers appearing on the two dice are different,then what is the probability that the sum is $6$?

If $A$ and $B$ are two events such that $P(A) = \frac{1}{4}$,$P(B) = \frac{1}{2}$,and $P(A \cap B) = \frac{1}{8}$,find $P(\text{not } A \text{ and not } B)$.

The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$,what is the probability of passing the Hindi examination?

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

If $x$ is chosen at random from the set $\{1, 2, 3, 4\}$ and $y$ is chosen at random from the set $\{5, 6, 7\}$,then the probability that $xy$ will be even is