Given two independent events $A$ and $B$ such that $P(A) = 0.3$ and $P(B) = 0.6$,find $P(A \text{ and } B)$.

$A$ and $B$ are independent events. Their probabilities are $3/10$ and $2/5$ respectively. What is the probability that exactly one of the events occurs?

$A$ 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?

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) = $ . . . . . . .

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.

Two coins and one die are tossed. What is the probability of getting heads on both coins and $3$ or $6$ on the die?