Jenna teaches two courses in second semester, MTH1122 and MTH1030. Among
Jenna students 20 percent are MTH1122 students. As a consequence of Jenna’s
teaching technique 10 percent of the MTH1030 students and 5 percent of the MTH1122
students develop an addiction to mathematics (wishful thinking, or course, but...).
a) What is the probability that one of Burkard’s students who has been randomly chosen
is a matheholic?
b) One of Jennas students presents at the doctors with acute symptoms of maths addiction.
What is the probability that this student is an MTH1030 matheholic? Assumptions: A student who takes one course, does not take the other course. There
were no matheholics among the students before Jenna started teaching the course.

2. Hello, sinyoungoh!

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

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?
Let $MH$ = "is a matheholic."

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

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

Therefore: . $P(MH) \:=\:0.01 + 0.08 \:=\:\boxed{0.09}$

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

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

We want: . $P(Y\,|\,MH)$

Bayes' Theorem: . $P(Y\,|\,MH) \;=\;\frac{P(Y \wedge MH)}{P(MH)} \;=\;\frac{0.08}{0.09} \;=\;\boxed{\frac{8}{9}}$