Have I solved the following problem correctly. Need guidance if I have attempted wrong, I am not sure.
In a class $60\%$ of students and $52\%$ of students physics. Out of the students who enjoy mathematics, $20\%$ do not enjoy physics. For the student who enjoy physics, what is the probability they do not like mathematics.
My calculations:
Let $M$ be the event of students who like mathematics and $P$ be the event of student who like physics then according to given problem we have the following data:
$n(M)=60\%=0.6$
$n(P)=52\%=0.52$
$n(M\cap P^\complement)=20\%=0.2$
Also we have: $n(M)-n(M\cap P^\complement)=n(M\cap P)$; putting value we get:
$n(M\cap P)=40\%=0.4$ (which is percent of students who like both physics and math)
Similiary:
$n(P\cap M^\complement)=n(P)-n(M\cap P)=12\%=0.2 $ (which is set of students who like physics but not math)
Now let $A$ represent event of students who like physics but not math, and $B$ be event of students who like physics; then by conditional probability: Following is the way we calculate the probability of students who like physics but not mathematics, as per requirement of the problem
$P(A/B)=N(A\cap B)/N(B)$
Since $A<B$
$N(A\cap B)=0.12$
Hence: $P(A/B)= 0.12/0.52=0.23076923076$