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 be a black card (i.e.,a club or a spade).

Let the sum of two positive integers be $24$. If the probability,that their product is not less than $\frac{3}{4}$ times their greatest positive product,is $\frac{m}{n}$,where $\operatorname{gcd}(m, n)=1$,then $n-m$ equals :

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,then the probability of happening neither $A$ nor $B$ is

$A$ bag contains $3$ red and $5$ black balls and a second bag contains $6$ red and $4$ black balls. $A$ ball is drawn from each bag. The probability that one is red and the other is black is:

If $A$ and $B$ are any two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,then the events $A$ and $B$ are

$A$ box $P$ contains one white ball,three red balls and two black balls. Another box $Q$ contains two white balls,three red balls and four black balls. If one ball is drawn at random from each one of the two boxes,then the probability that the balls drawn are of different colour is