In a class of 60 students, 40 are Democrats, 10 are business majors, and 4 of the business majors are Democrats. If one student is randomly selected from the class, find the probability o choosing a Democrat or a business major. P(Democrat or business major) = \( \square \) (Simplify your answer. Type an integer or a simplified fraction.)

To find the probability of choosing a Democrat or a business major, we will use the principle of inclusion-exclusion. First, let’s find the total number of Democrats (D) and business majors (B): - Total Democrats, D = 40 - Total Business Majors, B = 10 - Business Majors who are Democrats, D ∩ B = 4 Now we can use the formula: \[ P(D \cup B) = P(D) + P(B) - P(D \cap B) \] Calculating each term: - \( P(D) = \frac{40}{60} = \frac{2}{3} \) - \( P(B) = \frac{10}{60} = \frac{1}{6} \) - \( P(D \cap B) = \frac{4}{60} = \frac{1}{15} \) Now substituting into the formula: \[ P(D \cup B) = \frac{2}{3} + \frac{1}{6} - \frac{1}{15} \] To add these fractions, we need a common denominator. The least common multiple of 3, 6, and 15 is 30. Converting each term: - \( P(D) = \frac{2}{3} = \frac{20}{30} \) - \( P(B) = \frac{1}{6} = \frac{5}{30} \) - \( P(D \cap B) = \frac{1}{15} = \frac{2}{30} \) Now we can substitute back into the equation: \[ P(D \cup B) = \frac{20}{30} + \frac{5}{30} - \frac{2}{30} = \frac{23}{30} \] Therefore, the probability of choosing a Democrat or a business major is \[ P(Democrat \text{ or } business \text{ major}) = \frac{23}{30} \]