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

If $A$ and $B$ are two independent events and $P(A)=\frac{3}{5}$ and $P(B)=\frac{2}{3}$,then $P(A' \cap B')=$

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

$A$ 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:

If $P(A_1 \cup A_2) = 1 - P(A_1^c) P(A_2^c)$,where $c$ stands for complement,then the events $A_1$ and $A_2$ are

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