Let $A$ and $B$ be two events such that $P(A) = \frac{3}{8}$, $P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$. Then $P(A'|B) - P(A|B) =$ . . . . . .

If $A$ and $B$ are any two events of a random experiment and $P(B) \neq 1$,then $P(A | B^c) =$ ?

If $P(A)=0.8, P(B)=0.5$ and $P(B | A)=0.4,$ find $P(A | B).$

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

Let $X$ be the set of all five-digit numbers formed using $1, 2, 2, 2, 4, 4, 0$. For example,$22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that an element chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the value of $38p$ is equal to

$A$ coin is tossed three times. If event $E$ represents getting at least two heads and event $F$ represents getting a head on the first toss,find $P(E|F)$.