$A$ couple has two children. Find the probability that both children are females,if it is known that the elder child is a female.

For two events $A$ and $B$,$P(B) \neq 0$ and $P(A \mid B) = 1$,then . . . . . . .

Bag $P$ contains $3$ white, $2$ red, $5$ blue balls and bag $Q$ contains $2$ white, $3$ red, $5$ blue balls. $A$ ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red ball is

Assume that each born child is equally likely to be a boy or a girl. If a family has two children,what is the conditional probability that both are girls given that the youngest is a girl?

Two persons $P$ and $Q$ are considering applying for a job. The probability that $P$ applies for the job is $1/4$,the probability that $P$ applies for the job given that $Q$ applies for the job is $1/2$,and the probability that $Q$ applies for the job given that $P$ applies for the job is $1/3$. Then the probability that $P$ does not apply for the job given that $Q$ does not apply for the job is

Let $A$ and $B$ be two events such that $P(A) = \frac{5}{11}$, $P(B) = \frac{2}{11}$, and $P(A \cup B) = \frac{3}{11}$, then $P(A'|B')$ is . . . . . . .