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

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

Consider two events $A$ and $B$ such that $P(A) = \frac{1}{4}$,$P(B/A) = \frac{1}{2}$,$P(A/B) = \frac{1}{4}$. For each of the following statements,which is true?
$I.$ $P(A^c/B^c) = \frac{3}{4}$
$II.$ The events $A$ and $B$ are mutually exclusive
$III.$ $P(A/B) + P(A/B^c) = 1$

One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
$E:$ 'the card drawn is a spade'
$F:$ 'the card drawn is an ace'

If $P(E)=0.8, P(F)=0.5$ and $P(F \mid E)=0.4$ then,$P(E \mid F)=$ . . . . . . .

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, \ldots, 49$. The probability that the sum of the digits on the selected ticket is $8$,given that the product of these digits is zero,equals: