An urn contains $10$ black and $5$ white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

$A$ 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.

$A$ purse contains $4$ copper coins and $3$ silver coins. $A$ second purse contains $6$ copper coins and $4$ silver coins. $A$ purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?

Two marbles are drawn in succession from a box containing $10$ red,$30$ white,$20$ blue and $15$ orange marbles,with replacement being made after each drawing. Then the probability,that the first drawn marble is red and the second drawn marble is white,is

If $A_1$ and $A_2$ are independent events and $P(A_1 \cup A_2) = 0.5$ and $P(A_1) = 0.2$,then $P(A_2) = $ . . . . . . .

$A$ 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?