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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?

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    I suggest drawing up a Venn diagram and reason using that. That should help intuition. – 2017-02-06
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    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? – 2017-02-06

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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))

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    should it be 1/4 ? since (0.25 * 0.30 )/0.30? – 2017-02-06
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    The events are not independent; you are told that 10% of students major in Business and Math. – 2017-02-06
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    thanks. I now understand the problem. Quick question though, what do you call this specific type of probability? Is it conditional? – 2017-02-06
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    Yes, it's conditional. – 2017-02-06
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I do not agree with the answer given above. The problem guarantees that the selected student studies BM, that means he is one of the 40% that studies either BM solely or BM+Math.

Now the universe we're supposed to work is composed by this 40 students (let's say there are 100 of them total). Inside this group, 10 of the students with also study Math, so the probability will be $\frac{10}{40} = \frac{1}{4}$.

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    Your solution is correct if the wording in the problem is meant to specify that 30% Business students refers to 30% study Buisness but not Math. – 2017-02-06
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    I see your point – 2017-02-06