Question

at a local college, 100 students were asked about their major fields of study. the results are shown below. what is the probability that a randomly selected student is a female or a liberal arts major?
majors at local college

	mathematics/science	liberal arts	business studies
female	15	18	17

Explanation:

Step1: Find total number of students

Total students = 100 (given).

Step2: Find number of females

Females: \(15 + 18 + 17 = 50\)

Step3: Find number of Liberal Arts majors

Liberal Arts: \(20 + 18 = 38\)

Step4: Find number of female Liberal Arts majors (overlap)

Female Liberal Arts: \(18\)

Step5: Apply inclusion - exclusion principle

\(P(\text{Female or Liberal Arts})=\frac{\text{Number of Females}+\text{Number of Liberal Arts}-\text{Number of Female Liberal Arts}}{\text{Total}}\)
\(=\frac{50 + 38 - 18}{100}=\frac{70}{100}=0.7\)

Answer:

\(0.7\)