Question

In a class with 50 students, 25 of the students aresophomores, 15 of the students are mathematicsmajors, and 10 of the mathematics majors aresophomores. If a student in the class is to beselected at random, what is the probability thatthe student selected will be a sophomore or amathematics major or both?

Answer 1

Given:

To Determine: The probability that a student selected at random will be a sophomore or a mathematics major or both

The probability would be

`\begin{gathered} P(S,or,M,or,\text{both)}=\frac{n(S)+n(M)+n(\text{both)}}{n(\text{total)}} \\ P(S,or,M,or,\text{both)}=(15+5+10)/(50) \\ P(S,or,M,or,\text{both)}=(30)/(50) \\ P(S,or,M,or,\text{both)}=(3)/(5) \end{gathered}`

Hence, the probability of that a student selected at random will be a sophomore or a mathematics major or both is 3/5