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?
2
-
$\begingroup$ I suggest drawing up a Venn diagram and reason using that. That should help intuition. $\endgroup$– CasperFeb 6, 2017 at 13:23
-
1$\begingroup$ 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? $\endgroup$– luluFeb 6, 2017 at 13:23
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
4
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))
answered Feb 6, 2017 at 13:21
-
$\begingroup$ should it be 1/4 ? since (0.25 * 0.30 )/0.30? $\endgroup$– CodexFeb 6, 2017 at 13:32
-
$\begingroup$ The events are not independent; you are told that 10% of students major in Business and Math. $\endgroup$ Feb 6, 2017 at 13:33
-
$\begingroup$ thanks. I now understand the problem. Quick question though, what do you call this specific type of probability? Is it conditional? $\endgroup$– CodexFeb 6, 2017 at 13:36
-