$A$ bag contains $3$ white and $5$ black balls. If one ball is drawn,then the probability that it is black,is

Two integers are chosen at random and multiplied. The probability that the product is an even integer is

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S = \{x \in \mathbb{Z} : x(66 - x) \geq \frac{5}{9} M\}$ and the event $A = \{x \in S : x \text{ is a multiple of } 3\}$. Then $P(A)$ is equal to

$A$ 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?

What is the probability of getting a doublet when two dice are thrown?

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is