Question

a university tracks students preferences for study methods. the data is shown below: chart with columns study alone, study in groups, study online, total; rows undergraduates, graduates, total what is the probability that a randomly selected student either studies alone or is a graduate student? options: 25/75, 25/50, 125/150, 25/150, 100/150

Explanation:

Step1: Define events and formula

Use the addition rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, where $A$ = studies alone, $B$ = graduate student.

Step2: Calculate $P(A)$

Total students = 150, students who study alone = 75.
$P(A) = \frac{75}{150}$

Step3: Calculate $P(B)$

Total graduate students = 50.
$P(B) = \frac{50}{150}$

Step4: Calculate $P(A \cap B)$

Graduates who study alone = 25.
$P(A \cap B) = \frac{25}{150}$

Step5: Compute final probability

Substitute values into the formula:
$P(A \cup B) = \frac{75}{150} + \frac{50}{150} - \frac{25}{150} = \frac{75+50-25}{150} = \frac{100}{150}$

Answer:

100/150