Hello, sinyoungoh!

There's far too much information; I'll pare it down.

Let = "is a matheholic."Jenna teaches two courses, course X and course Y.

20 percent of her students are in X. As a consequence of Jenna’s teaching technique,

5% of X students and 10% of the Y students are matheholics.

a) What is the probability that one of Burkard’s students . . . who?

who has been randomly chosen is a matheholic?

0.20)(0.05) \:=\:0.01" alt="P(X \wedge MH) \:=\0.20)(0.05) \:=\:0.01" />

0.80)(0.10) \:=\:0.08" alt="P(Y \wedge MH) \:=\0.80)(0.10) \:=\:0.08" />

Therefore: .

b) One of Jenna's students is a matheholic.

What is the probability that this student is in course Y?

We want: .

Bayes' Theorem: .