Quote:

Of a class of 100 students 80 attend lectures.

The whole class is made to sit a multiple-choice test.

On the first question, any student who has attended lectures knows the answer.

The other students each know the answer with probability 1/2.

Any student who knows the answer gets it right.

A student who does not know, picks an answer at random from the 3 choices offered.

The teacher selects a student who has answered the first question correctly.

Show that the probability that the student attended lectures is 6/7.