Question

in a class of 60 students, 44 are democrats, 6 are business majors, and 5 of the business majors are democrats. if one student is randomly selected from the class, find the probability of choosing a democrat or business major. p(democrat or business major) = (simplify your answer. type an integer or a simplified fraction.)

Explanation:

Step1: Use the inclusion - exclusion principle for probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, let $A$ be the event of being a Democrat and $B$ be the event of being a business major.
We know that $n(A) = 44$, $n(B)=6$, $n(A\cap B)=5$ and $n(S)=60$ (where $n(S)$ is the total number of students in the class).
$P(A)=\frac{n(A)}{n(S)}=\frac{44}{60}$, $P(B)=\frac{n(B)}{n(S)}=\frac{6}{60}$ and $P(A\cap B)=\frac{n(A\cap B)}{n(S)}=\frac{5}{60}$.

Step2: Calculate $P(A\cup B)$

$P(A\cup B)=\frac{44 + 6- 5}{60}=\frac{45}{60}=\frac{3}{4}$

Answer:

$\frac{3}{4}$