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 male 16 20 14 female 15 18 17

Explanation:

Step1: Define events and formula

Use the addition rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, where $A$ = female, $B$ = liberal arts major.

Step2: Calculate total female students

Sum all female majors: $15 + 18 + 17 = 50$
$P(A) = \frac{50}{100}$

Step3: Calculate total liberal arts majors

Sum all liberal arts majors: $20 + 18 = 38$
$P(B) = \frac{38}{100}$

Step4: Calculate female liberal arts students

This is the overlap: $18$
$P(A \cap B) = \frac{18}{100}$

Step5: Compute final probability

Substitute values into the formula:
$P(A \cup B) = \frac{50}{100} + \frac{38}{100} - \frac{18}{100} = \frac{50+38-18}{100} = \frac{70}{100} = \frac{7}{10}$

Answer:

$\frac{7}{10}$