Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(A \cap B)$.

$A$ bag contains $16$ coins,of which $2$ are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is

$A$ woman has $10$ keys,out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) until she succeeds in opening the lock. What is the probability that the seventh key works?

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then,the probability for the ball chosen to be white is:

Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king,is

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 $p$.