Artificial intelligent assistant

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.

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