Question

in a class of 45 students, 25 are democrats, 10 are business majors, and 3 of the business majors are democrats. if one student is randomly selected from the class, find the probability of choosing a democrat or a business major.

p(democrat or business major) = \boxed{}
(simplify your answer. type an integer or a simplified fraction.)

Explanation:

Step1: Recall addition rule for probability

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

Step2: Identify values

$P(\text{Democrat}) = \frac{25}{45}$, $P(\text{business major}) = \frac{10}{45}$, $P(\text{both}) = \frac{3}{45}$

Step3: Calculate the result

$\frac{25}{45} + \frac{10}{45} - \frac{3}{45} = \frac{32}{45}$

Answer:

$\frac{32}{45}$