Question

Students received grades with or - (example B ). Of all students who received one or more plus grades, 92% were undergraduates and 8% were graduates. Of all students who received one or more minus grades, 93% were undergraduates and 7% were graduates. Find the probability that a student is an undergraduate student, given that the student received a plus grade.

Answer 1

The probability that a student is an undergraduate student, given that the student received a plus grade is 0.92

Explanation:

The conditional probability of an event B given that another event A has already occurred is:

`P(B|A)=(P(A\cap B))/(P(A))`

Denote the events as follows:

X = a students is a graduate

Y = a students is a under-graduate

+ = a student received one or more plus grades

- = a student received one or more minus grades

Consider the tree diagram below.

According to the tree diagram, the probability that a student is an undergraduate student, given that the student received a plus grade is:

P (+ | Y) = 0.92

Thus, the probability that a student is an undergraduate student, given that the student received a plus grade is 0.92.