# Probability problem with multiple percentages

At a university, 28% of the 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.

(a) What is the probability a randomly chosen student is male and majoring in zoology?

(b) What is the probability that one randomly selected student is a male or is majoring in zoology, or both?

(c) What proportion of males at the university are majoring in zoology?

(d) What proportion of students are male and are not majoring in zoology?

I'm not sure how to answer these questions so I would be grateful for some help! Thanks :)

At a university, 28% of the 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.

Write down what you do know.   $\mathsf P(Z)=0.28,$ and so on.

(a) What is the probability a randomly chosen student is male and majoring in zoology?

You seek $\mathsf P(M\cap Z)$.   Express that in terms of what you do know and evaluate.

$$\mathsf P(M\cap Z) = \mathsf P(M\mid Z)\;\mathsf P(Z)$$

And so forth.

• Thanks that helps a lot! I'm still unclear about part d, when Z complement gets thrown into the mix, would you know how to do that? I know that were trying to solve for P(Zc ∩ M) but I'm not sure how to do it – Kate.O Oct 13 '17 at 0:36