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 $P(\text{not } E \text{ and not } F)$.

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) = $

Statement $- I :$ If the probabilities of solving a problem by $A$ and $B$ are $1/3$ and $1/4$ respectively,then the probability that the problem is solved is $7/12$.
Statement $- II :$ The events described above are independent events.

The probability of an event happening is the square of the probability of a second event,but the odds against the first are the cube of the odds against the second. The probabilities of the events are:

If $A$ and $B$ are two independent events,then $P(A \cup B) = $

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