If $A$ and $B$ are independent events and $P(A)=\frac{2}{3}$ and $P(B)=\frac{3}{5}$,then $P(A^{\prime} \cap B)$ is equal to:

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

$A$ basket contains $5$ apples and $7$ oranges and another basket contains $4$ apples and $8$ oranges. If one fruit is picked out at random from each basket,then the probability of getting one apple and one orange is

The probability that India wins the toss is $3/4$. If it wins the toss,the probability of winning the match is $4/5$,otherwise it is $1/2$. Find the probability that India wins the match.

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

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