A student takes a multiple choice exam where each question h

A student takes a multiple choice exam where each question has four choices. The student has only learned 30% of the material. Thus there is a 30% chance that she will know the answer to a question. For the questions where she does not know the answer, there is a 25% chance she will guess correctly. If we choose a question at random from the exam, what is the probability that she will get it right?

I got 0.475 - but I\'m not sure that I\'m right! Thank you.

Solution

The probability that the question is from what she has learnt = 0.3

The probability that the question is from what she has not learnt = 0.7.

If she has learnt that question then she will definetely do it correctly and if she has not learnt that question then there is probability of 0.25 to guess it right.

So overall probability of getting correct answer = (0.3) (1) + (0.7) (0.25) = 0.3 + 0.175 = 0.475.

Hence, your answer is perfect.