$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find  $P \left( A ^{\prime} \cap B ^{\prime}\right)$.

Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is

If the odds in favour of an event be $3 : 5$, then the probability of non-occurrence of the event is

If $P\,({A_1} \cup {A_2}) = 1 – P(A_1^c)\,P(A_2^c)$ where $c$ stands for complement, then the events ${A_1}$ and ${A_2}$ are

If $P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$ and the events $A$ and $B$ are independent, then $x =$