Events $A$ and $B$ are independent events and $P(A)=P$,$P(B)=\frac{1}{2}$ and $P(A \cup B)=\frac{3}{5}$,then the value of $P$ is . . . . . . .

Two cards are drawn from a pack of well-shuffled $52$ playing cards one by one without replacement. The probability that both cards are queens is:

One bag contains $5$ white and $4$ black balls. Another bag contains $7$ white and $9$ black balls. $A$ ball is transferred from the first bag to the second and then a ball is drawn from the second. The probability that the ball drawn is white,is

$A$ bag contains $10$ white and $15$ red balls. If two balls are drawn one after another,what is the probability that the first ball is red and the second ball is white?

If $A$ and $B$ are independent events and $P(A)=\frac{2}{3}$ and $P(B)=\frac{3}{5}$,then $P(A^{\prime} \cap B)$ is equal to:

There are $3$ bags $A, B$ and $C$. Bag $A$ contains $2$ white and $3$ black balls,bag $B$ contains $4$ white and $2$ black balls and Bag $C$ contains $3$ white and $2$ black balls. If a ball is drawn at random from a randomly chosen bag,then the probability that the ball drawn is black,is