Let $A$ and $B$ be events for which $P(A) = x$,$P(B) = y$,and $P(A \cap B) = z$. Then $P(\bar{A} \cap B)$ equals:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $A$ and $B$.

If $A$ and $B$ are two events,what is the probability that exactly one of them occurs?

Each of the two boxes $A$ and $B$ contain $10$ chits numbered $1$ to $10$. If one chit is drawn at random from each of $A$ and $B$,then the probability that the number on the chit drawn from $A$ is smaller than the number on the chit drawn from $B$,is

$A$ person can hit a bird once in three attempts. If the person makes three attempts, what is the probability that the bird is hit (in $/27$)?

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is