a certain university, 30% of the students major in mathematics. Of the students majoring in mathematics, 60% are males. Of all the students at the university, 70% are males. A) What is the probability that a student selected at random in the university is male and majors in mathematics? B)What is the probability that a randomly selected student in the university is female or majors in mathematics or both?

Probability female OR majors in math:

P(F Or M)=P(F)+P(M)-P(F and M)

One thing to do is make a table. Assume 1,000 students for simplicity.

\begin{array}{c||c|c|c|c }\text{} & \text{Male} & \text{Female} & \text{Total}\\ \hline \text{math} & 180 & 120 & 300\\ \hline \text{not math} & 520 & 180 & 700\\ \hline \text{} & 700 & 300 & 1000 \end{array}

By looking at the table, we can answer any question.

i.e. probability a randomly chosen student is female given they major in math?

Go down the Female column to the Math row and go across.

We get 120/300=2/5=.60

Probability a student is male and majors in math:
180/1000=(.60)(.30)=.18