If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$,and $P(A \cap B) = \frac{1}{4}$,then find the value of $P(A' \cap B')$.

Let $A$ and $B$ be two events such that $P(A) = 0.3$ and $P(A \cup B) = 0.8$. If $A$ and $B$ are independent events,then $P(B) = $

Three critics review a book. For the three critics,the odds in favour of the book are $(5: 2)$,$(4: 3)$ and $(3: 4)$ respectively. The probability that the majority is in favour of the book is

If a number is selected from the first $30$ natural numbers,then the probability that the number selected is divisible by $4$ or $7$ is:

If $A$ and $B$ are two events such that $P(A \cup B) + P(A \cap B) = \frac{7}{8}$ and $P(A) = 2P(B)$,then $P(A) = $

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occur simultaneously is $0.16$. Then the probability that none of the two occurs is