In a statistics class of 41 students, the professor takes a survey about class l
ID: 3231745 • Letter: I
Question
In a statistics class of 41 students, the professor takes a survey about class level and major. Suppose a student is randomly selected from the class. Answer the following probability questions.
(a) What is the probability that the student is a nursing major?
(b) What is the probability that the student is a nursing major and a sophmore?
(c) What is the probability that the student is a nursing major or a sophmore?
(d) What is the probability that the student is a business or computer science major?
(e) What is the probability that the student is a business major given that the student is a junior?
Nursing Business Computer Science Freshmen 0 5 2 Sophmore 5 4 2 Junior 6 3 7 Senior 1 2 4Explanation / Answer
a) P(Nursing major) = (0 + 5 + 6 + 1) / 41 = 12/41
b) P(Nursing major and a sophomore = 5/41
c) P(Nursing major or a sophomore)
= P(Nursing major) + P(Sophomore) - P(Nursing major and sophomore)
= 12/41 + (5 + 4 + 2)/41 - 5/41
= 12/41 + 11/41 - 5/41
= 18/41
d) P(Business or computer science major) = 1 - P(Nursing major) = 1 - 12/41 = 29/41
e) P(Business major | Junior) = 3/(6 + 3 + 7) = 3/16