Question

Peer Teacher Mike only needs two more classes to graduate. So does Peer Teacher Shannon. Mike is enrolled in his Risk Capstone and Interdimensional Yoga. Shannon is enrolled in her Actuarial Capstone and Underwater Golf. Both students know that they will earn either an A or a C in each class. 3 Mike has a 90% chance for an A in Interdimensional Yoga (Mike is secretly a Yogi) and a 70% chance for an A in his Risk Capstone. Shannon has an 85% chance for an A in Underwater Golf and a 90% chance for an A in her Actuarial Capstone. Remember from a point system an A is worth 4 points and a C is worth 2.

a. What is Mike’s expected GPA this semester? (3 points)

b. What is Shannon’s expected GPA this semester? (3 points)

Answer 1

We can have four combination of the grades the first letter represents Risk capstone and 2nd interdimentionl yoga. Accordingly we can add the grade points. Since the classes are independent we mulptiply their probabilties of securing the grade for their intersection.

We have been given probabiities of A so to get the probability of 'C' we can just '1 - P(A) = P(C)'

Mike	Capstone	Points a	p c	Yoga	points b	P d	Points x (a+b)	Probability p  (c + d)	x P(x)
	A	4	70%	A	4	90%	8.00	0.63	5.04
	A	4	70%	C	2	10%	6.00	0.07	0.42
	C	2	30%	A	4	90%	6.00	0.27	1.62
	C	2	30%	C	2	10%	4.00	0.03	0.12
Total							24.00	1.00	7.20

(1)

(2)

Shannon	Capstone	Points	p	Golf	points	P	Points x	Probability p	x P(x)
	A	4	90%	A	4	85%	8.00	0.77	6.12
	A	4	90%	C	2	15%	6.00	0.14	0.81
	C	2	10%	A	4	85%	6.00	0.09	0.51
	C	2	10%	C	2	15%	4.00	0.02	0.06
Total							24.00	1.00	7.50