$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B | A)$ if $A \cap B = \phi$.

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

In a city,$40\%$ of the people have brown hair,$25\%$ have brown eyes,and $15\%$ have both brown hair and brown eyes. If a person is selected at random from those having brown hair,what is the probability that they also have brown eyes?

Given that $E$ and $F$ are events such that $P(E)=0.6$,$P(F)=0.3$,and $P(E \cap F)=0.2$,find $P(E|F)$ and $P(F|E)$.

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

If $A$ and $B$ are two events such that $P(A \cup B) = P(A \cap B)$,then the true relation is