Question

A statistics teacher knows from past experience that a student who does homework consistently has a probability of 0.95 of passing the examination , whereas a student who does not do homework has a probability of 0.30 of passing.

i) If 25% students in a large group of students do their homework consistently, what percentage can expect to pass?

ii) If a student chosen at random from the group gets a pass, what is the probability that the student has done the homework consistently?

Answer 1

The fraction of the students who does homework consistently and is expected to pass the exam is

$0.25\cdot 0.95 = 0.2375$

The fraction of the students who does not do homework consistently but is expected to pass the exam is $0.75\cdot 0.30 = 0.225$

The fraction of the students who is expected to pass the exam is 0.2375+0.225=0.4625

If a student chosen at random from the group gets a pass, then the probability that this student has done the homework consistently is 0.2375/0.4625=0.5135