Hello, apply-it!

Don't be embarrassed . . . Conditional probability is always tricky.

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.

Are you familiar with Bayes' Theorem? .

We want: .

[1] Determine the numerator.

. . .

Hence: .

[2] Determine the denominator.

. . .There arethreeways to get the correct answer.

(a) The student attended the class and got the right answer.

. . .We found this in part [1]: .

(b) The student did not attend but knew the answer.

. . .

. . .Hence: .

(c) The student did not attend, did not know the answer, and guessed correctly.

. .

. . .Hence: .

Then: .

Therefore: . . . . . ta-DAA!