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:

$A$ bag $X$ contains $2$ white and $3$ black balls,and another bag $Y$ contains $4$ white and $2$ black balls. If one bag is selected at random and one ball is drawn from it,what is the probability that the ball is white?

$A$ basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. If one fruit is picked out at random from each basket,then the probability of getting one apple and one orange 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?

From a pack of $52$ cards,two cards are drawn in succession one by one without replacement. The probability that both are aces is

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that the first ball is black and the second is red.