Question

students apply for admission to different academic programs within a college. because of space, each program can only accept a limited number of students. the table below shows the acceptance data for a selection of majors in the college. what is the probability that a student was accepted, given that the student applied to the business program? college major total spanish business chemistry accepted 182 45 65 72 rejected 68 15 35 18 total 250 60 100 90

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of a two - way table, if $A$ is the event of being accepted and $B$ is the event of applying to the business program, then $P(A|B)=\frac{\text{Number of students accepted to business}}{\text{Total number of students applying to business}}$.

Step2: Identify relevant values from the table

The number of students accepted to the business program is 65, and the total number of students applying to the business program is 100.

Step3: Calculate the probability

$P=\frac{65}{100}=0.65 = 65.0\%$

Answer:

65.0%