$3 P(A) = P(B) = \frac{5}{13}$ and $P(A \mid B) = \frac{3}{5}$,then $P(A \cup B) = $ . . . . . . .

Which of the following is a homogeneous differential equation?

When $3$ dice are thrown at a time, the sum of the numbers appeared on $3$ dice was found to be $15$. Then the probability that the number $5$ does not appear on any one of the dice is

An unbiased coin is tossed $3$ times. If the third toss results in a head,what is the probability of getting at least one more head in the first two tosses?

If $2 P(A) = P(B) = \frac{5}{13}$ and $P(A \mid B) = \frac{2}{5}$,then $P(A \cup B) =$ . . . . . . .

The equation of the curve satisfying $x dy - y dx = \sqrt{x^2 - y^2} dx$ with the condition $y(1) = 0$ is: