The odds in favour of drawing a king from a pack of $52$ playing cards is

If the odds against $A$ solving a problem are $4:3$ and the odds in favor of $B$ solving the problem are $7:5$,what is the probability that only one of them solves the problem?

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

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

$A$ card is drawn from a pack of $52$ cards. Find the probability that the card will be a queen or a heart.

The odds against a certain event are $5: 2$ and the odds in favour of another independent event are $6: 5$. The probability that at least one of the events will happen,is