If $A$ and $B$ are two independent events,then the probability of occurrence of at least one of $A$ and $B$ is given by $1 - P(A') P(B')$. Is this statement true or false?

If $E$ and $F$ are events such that $P(E) = \frac{1}{4}$,$P(F) = \frac{1}{2}$ and $P(E \cap F) = \frac{1}{8}$,find $P(E \cup F)$.

If $A$ and $B$ are two events in a random experiment such that $P(A) + P(B) = 2 P(A \cap B)$, then:

If $A$ and $B$ are independent events such that odds in favour of $A$ is $2:3$ and odds against $B$ is $4:5$,then $P(A \cap B)=$

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

In an entrance test that is graded on the basis of two examinations,the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?