Two urns identical in appearance contain respectively $3$ green and $2$ black balls and $2$ green and $5$ black balls. One urn is selected at random and a ball is drawn from it. The probability that it is black is

$A$ box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good,the box is approved for sale; otherwise,it is rejected. Find the probability that a box containing $15$ oranges,out of which $12$ are good and $3$ are bad,will be approved for sale.

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 $B$ contains $4$ white balls and $2$ black balls. Another bag $C$ contains $3$ white balls and $5$ black balls. If one ball is drawn randomly from each bag, then the probability that the two balls drawn are both white is

$A$ 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

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.