Question

According to the general equation for conditional probability if p (a^b) = 3/4 and p (b) = 4/5 what is p (a/b)

Answer 1

I'm guessing "a^b" is meant to denote the intersection, or possibly $A^B$ which could be the complement of $B$ in $A$. I'll stick with the first assumption. I'll also read "a/b" as $A\mid B$, the event of $A$ being conditioned on $B$, though this also is ambiguous and could refer to the complement of B in A.

By definition of conditional probability,

$\mathbb P(A\mid B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)}=\dfrac{\frac34}{\frac45}=\dfrac{15}{16}$