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? 26.0% 35.0% 35.7% 65.0%

Explanation:

Step1: Recall the formula for conditional probability

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

Step2: Identify the relevant values from the table

From the table, the number of students accepted into the business program is \(65\), and the total number of students who applied to the business program is \(100\).

Step3: Calculate the probability

Using the formula \(P=\frac{65}{100}=0.65\). To convert this to a percentage, we multiply by \(100\), so \(0.65\times100 = 65\%\).

Answer:

65.0%