$A$ bag $X$ contains $2$ white and $3$ black balls,and another bag $Y$ contains $4$ white and $2$ black balls. If one bag is selected at random and one ball is drawn from it,what is the probability that the ball is white?

When a missile is fired from a ship,the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target,given that it is not intercepted,is $\frac{3}{4}$. If three missiles are fired independently from the ship,then the probability that all three hit the target is:

The probability that a certain beginner at golf gets a good shot if he uses the correct club is $\frac{1}{3}$ and the probability of a good shot with an incorrect club is $\frac{1}{4}$. In his bag are $5$ different clubs,only one of which is correct for the shot in question. If he chooses a club at random and takes a stroke,then the probability that he gets a good shot,is

$A$ bag contains $4$ red and $3$ black balls. $A$ second bag contains $2$ red and $3$ black balls. One bag is selected at random. If from the selected bag,one ball is drawn at random,then the probability that the ball drawn is red,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.

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) = $ . . . . . . .