Question:
In class of 125 students, in examination 70 students passed in mathematics and 55 students passed in statistics and 30 passed in both the subject.
Find the probability of the event where selected student has passed only in one subject.
My Efforts:
$P(M\ \cup\ S) = P(M) + P(B)- P(M\ \cap\ S) $
$P(M\ \cup\ S) = 70 + 55 - 30 = 95 $
So answer is $\frac{95}{125}= \frac{19}{25}=0.76$
But answer given is $\frac{13}{25}= 0.52$
I know i am missing something, but can't figure out what?
What you're looking for is called the symmetric difference. Namely, $$A \triangle B = (A\cup B) - (A\cap B).$$
It's the union without the intersection. If the left circle represents those passing math, and the right circle represents those passing stats, and we don't want those who passed both, we want to find the probability of the symmetric difference of the two.
You already found $P(M \cup S)$. Now you just need to subtract the probability of the intersection of the two.