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

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) = $ . . . . . . .

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

$A$ pandemic has been spreading all over the world. The probabilities are $0.7$ that there will be a lockdown,$0.8$ that the pandemic is controlled in one month if there is a lockdown,and $0.3$ that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month 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?

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