$A, B, C$ are any three events. If $P (S)$ denotes the probability of $S$ happening then $P\,(A \cap (B \cup C)) = $
$P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C)$
$P(A) + P(B) + P(C) - P(B)\,P(C)$
$P(A \cap B) + P(A \cap C) - P(A \cap B \cap C)$
None of these
The probability that a leap year selected at random contains either $53$ Sundays or $53 $ Mondays, is
Prove that if $E$ and $F$ are independent events, then so are the events $\mathrm{E}$ and $\mathrm{F}^{\prime}$.
If $P(A) = \frac{1}{2},\,\,P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{7}{{12}},$ then the value of $P\,(A' \cap B')$ is
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.4$, $P ( A \cap B )=0.8$
For three events $A,B $ and $C$ ,$P ($ Exactly one of $A$ or $B$ occurs$)\, =\, P ($ Exactly one of $C$ or $A$ occurs $) =$ $\frac{1}{4}$ and $P ($ All the three events occur simultaneously $) =$ $\frac{1}{16}$ Then the probability that at least one of the events occurs is :