Let $0 < P(A) < 1$,$0 < P(B) < 1$ and $P(A \cup B) = P(A) + P(B) - P(A)P(B).$ Then

Let $S$ be the sample space of a random experiment and $P$ be a probability function defined on the power set of $S$. Two events $A$ and $B$ of the random experiment are called independent if

$A$ boy throws an unbiased die. Whenever he gets $1$ on the die,he has a further chance to throw it once again immediately. The probability that the boy gets a score of $7$ in this process is

$A$ coin is tossed $2020$ times. The probability of getting head on $1947^{\text{th}}$ toss is

Let $A$ and $B$ be two events such that $P(A \cap B) = \frac{1}{6}$,$P(A \cup B) = \frac{31}{45}$,and $P(\bar{B}) = \frac{7}{10}$. Then which of the following is true?

$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?