The probabilities of two events $A$ and $B$ are $0.25$ and $0.50$ respectively. The probability of both $A$ and $B$ occurring simultaneously is $0.14$. What is the probability that neither $A$ nor $B$ occurs?

Three groups of children $A$, $B$, and $C$ contain boys and girls as given below. Group $A$ contains $3$ girls and $1$ boy, group $B$ contains $2$ girls and $2$ boys, and group $C$ contains $3$ boys and $1$ girl. If $1$ child is selected at random from each group, what is the probability that the three children selected consist of $1$ girl and $2$ boys?

$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of the numbers that turn up is $12$.

$A$ coin is tossed three times. Consider the following events:
$A$: 'No head appears',
$B$: 'Exactly one head appears',
$C$: 'At least two heads appear'.
Do they form a set of mutually exclusive and exhaustive events?

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

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will not be a diamond.