$A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{3}$. Then $P$ (neither $A$ nor $B$) is equal to

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then,the probability for the ball chosen to be white is:

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

$A$ bag contains $4$ red and $3$ blue balls. Two balls are drawn one after another. If the first ball is replaced before drawing the second,what is the probability that the first ball is red and the second ball is blue?

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

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: