At a certain university, 28% of students major in zoology. Of all the students majoring in zoology, 68% are males. It is also known that 56% of all students at the university are male. Let Z represent the event that a randomly chosen student is majoring in zoology. Let M represent the event that a randomly chosen student is male. What proportion of males at the university are majoring in zoology?

Previously solved for P(M∩Z)=0.1904 and this is correct. I've tried P(Z|M) = P(M∩Z) / P(Z), and get the answer 0.68 which is the probability that a student majoring in zoology is a male. The correct answer is 0.34, which is exactly half, but I am not sure how to get this answer.

Any help is appreciated!

  • 1
    $\begingroup$ The equation $P(Z\vert M) = P(M\cap Z) / P(Z)$ is equivalent to $P(Z)P(Z\vert M) = P(M\cap Z)$, which is not correct. stattrek.com/probability/probability-rules.aspx $\endgroup$ – mathmandan Nov 5 '15 at 16:00
  • $\begingroup$ Thank you, I took a look at the site and found where I went wrong. $\endgroup$ – Astag Nov 5 '15 at 16:10
  • $\begingroup$ Great! Glad you found the solution! $\endgroup$ – mathmandan Nov 5 '15 at 16:11

Let it be that there are $10000$ students in total.

Then $2800$ of them major in zoology and $68\times28=1904$ of these are male.

Also it is known that $5600$ of all students are male.

So the proportion of males majoring in zoology is: $$\frac{1904}{5600}$$

  • $\begingroup$ Thank you very much for the further explanation. $\endgroup$ – Astag Nov 5 '15 at 16:24
  • $\begingroup$ You are welcome. Nice to see that you found it yourself. $\endgroup$ – drhab Nov 5 '15 at 16:26

Thanks to mathmandan I found my error and got the right answer.

P(Z|M) = P(M∩Z) / P(M) = 0.1904/0.56 = 0.34

Should have been divided by P(M), not P(Z).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.