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

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:

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

$A$ bag contains $9$ discs of which $4$ are red,$3$ are blue,and $2$ are yellow. The discs are similar in shape and size. $A$ disc is drawn at random from the bag. Calculate the probability that it will be either red or blue.

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 $B$ and $C$.

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is