Question

12. In a Biology class 85% of students pass the midterm exam. If a student passes the midterm exam, there is a 75% they pass the final. If a student does not pass the midterm exam, there is a 55% chance of passing the final exam. a. [3] What is the probability that a student passes both exams? b. [3] If a student passes the final, what is the probability that they passed the midterm exam? C. [3] Are the events a student passes the midterm, a student passes the final independent events? You must show the reason for your answer and it must make sense, in order to get credit.

Answer 1

Contingency table based on information:

data	Prob	pass final	Prob of pass final	Prob of do not pass final
pass midT	0.8500	0.7500	0.6375	0.2125
Do no pass midT	0.1500	0.5500	0.0825	0.0675
Total	1.0000	-	0.7200	0.2800

(a) P(student passes both exam) = 0.85 * 0.75 = 0.6375

(b) P(passed midT / pass final) = (passed midT & passed final) P( passed final) = 0.6375 / 0.7200

P(passed midT / pass final) = 0.8854

(c) Events are independent if the outcome of one event does not affect the outcome of other;

i.e. P( A & B) = P(A) * P(B)

P(student passing midT & student passing final) is not correct as % of student passing final depends on passing or not passing midT.

Hence the events are dependent :

P( A & B) = P(A) * P(B/A)

for eg:

P(passed midT / pass final) = (passed midT & passed final) / P(passed final) = 0.6375 / 0.7200

P(passed midT / pass final) = 0.8854