If $A_i$ $(i=1, 2, 3, \ldots, n)$ are $n$ independent events with $P(A_i) = \frac{1}{1+i}$ for each $i$,then the probability that none of $A_i$ occurs is

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

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

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.

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