Describe the sample space for the indicated experiment: $A$ coin is tossed and a die is thrown.

$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace.

$A$ bag contains $5$ black balls, $4$ white balls and $3$ red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved if both of them try independently is

Two brothers $X$ and $Y$ appeared for an exam. Let $A$ be the event that $X$ has passed the exam and $B$ is the event that $Y$ has passed. The probability of $A$ is $\frac{1}{7}$ and of $B$ is $\frac{2}{9}$. Then,the probability that both of them pass the exam is

If $A$ and $B$ are events having probabilities $P(A)=0.6$, $P(B)=0.4$, and $P(A \cap B)=0$, then the probability that neither $A$ nor $B$ occurs is