The event $A$ is independent of itself if and only if $P(A) = $

If $P(A) = 0.65$ and $P(B) = 0.15$,then $P(\bar{A}) + P(\bar{B}) = $

$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.

$A$ bag $A$ contains $2$ white and $3$ red balls and bag $B$ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $B$ is:

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. What is the probability that the problem is solved?

If a committee of $3$ is to be chosen from a group of $38$ people of which you are a member,what is the probability that you will be on the committee?