University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some students get a Bachelor of Arts and Science degree, which requires meeting graduation criteria for both degrees. A student advisor needs to know the probability a newly admitted student is interested in such a program, so that the student can be properly advised. A study of previous years finds that the probability a student gets a Bachelor of Science degree is P(Science) = 0.3 and the probability a student gets a Bachelor of Arts degree is P(Arts) = 0.6. The study also shows that the probability a student gets no degree is P(no) = 0.2. The probability a student gets a Bachelor of Arts and Science degree is:
A)0.2.
B)0.3.
C)0.1.
D)0.6.

Question

Quizplus · Accepted Answer

The probability of a student obtaining both degrees is not given directly. Therefore, we cannot assume that it is the sum of the probabilities of obtaining each degree separately. Instead, we must use the formula P(A ∩ B) = P(A) + P(B) - P(A ∪ B), where A and B are events representing the student obtaining a Bachelor of Arts degree and a Bachelor of Science degree, respectively. We are given P(A) = 0.6, P(B) = 0.3, and P(no) = 0.2. Using the formula, we have P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.6 + 0.3 - 1 = -0.1. Since probabilities cannot be negative, we conclude that P(A ∩ B) = 0. Therefore, the probability a student gets a Bachelor of Arts and Science degree is 0.1.

University Degree Requirements Typically Are Different for Bachelor of Science