If $A$ and $B$ are two events such that $P(A) = 0.4$ , $P\,(A + B) = 0.7$ and $P\,(AB) = 0.2,$ then $P\,(B) = $

The probabilities that a student passes in Mathematics, Physics and Chemistry are $m, p$ and $c$ respectively. On these subjects, the student has a $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ chance of passing in exactly two. Which of the following relations are true

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

Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random Find the probability that she reads neither Hindi nor English newspapers.

If $P\,(A) = \frac{1}{4},\,\,P\,(B) = \frac{5}{8}$ and $P\,(A \cup B) = \frac{3}{4},$ then $P\,(A \cap B) = $