# Probability problem (University course)

In a university, $30$% of the students major in Business Management, $25$% major in mathematics, and $10$% major in both Business Management and Mathematics. A student from this university is selected at random. If the student majors in Business Management, what is the probability that he/she also majors in Mathematics? I've come up with the solution of by adding them both $.30$+$.25$ and then multiply $.10$. Am I missing something or did I come up with the wrong solution?

• I suggest drawing up a Venn diagram and reason using that. That should help intuition. Feb 6, 2017 at 13:23
• For intuition: Say there are exactly $100$ students. Of these, we must have $10$ who major in both, $20$ who major in Business only, $15$ that major in Math only and $55$ who do neither. Does that clarify matters?
– lulu
Feb 6, 2017 at 13:23

We are actually looking for the probability that someone majors in both courses over the probability that someone majors in Buisness. This is obviously $\frac{1}{3}=33%.$ The reason your answer is incorrect is because the total probability of someone majoring in math is irrelevant; the people majoring in Math but not Buisness Management are not our concern.
(In general you can use $P(A|B)=\frac{P(A and B)}{P(B)}$. We're looking for P(Math|Buisness))