If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$,find $P(A \cap B)$ if $A$ and $B$ are independent events.

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.

$A$ bag contains $4$ red and $3$ black balls. $A$ second bag contains $2$ red and $3$ black balls. One bag is selected at random. If from the selected bag,one ball is drawn at random,then the probability that the ball drawn is red,is

For independent events $A$ and $B$,$P(A) = \frac{1}{3}$,$P(A \cup B) = \frac{2}{5}$,and $P(B) = p$. Find the value of $p$.

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

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