Question

You study for an exam, but due to the fact that you waited too long, you only learn 30% of the material. The exam is all multiple choice, with each question having 4 choices.

a) If you come across a question for which you don't know the answer, what's the probability of getting the answer right?

b) If you come across a question for which you do know the answer, what's the probability of getting it right (hint: don't “over think” this - what does it mean if you know the answer...)?

c) What is the overall probability of getting any question correct?

Answer 1

a) If you come across a question for which you don't know the answer, what's the probability of getting the answer right?

Since there are 4 choice

P[ not knowing the answer getting the answer right ] = 1/4

b) If you come across a question for which you do know the answer, what's the probability of getting it right?

Since I know the answer

P[ knowing the answer getting the answer right ] = 1

c) What is the overall probability of getting any question correct?

P[ Knowing the answer ] = 30% = 0.3

P[ Not knowing the answer ] = 1 - 0.3 = 0.7

P[ Getting any question correct ] = P[ Knowing the answer ]*P[ knowing the answer getting the answer right ] + P[ Not knowing the answer ]*P[ not knowing the answer getting the answer right ]

P[ Getting any question correct ] = 0.3*1 + 0.7*(1/4)

[ Getting any question correct ] = 0.3 + 0.175

[ Getting any question correct ] = 0.475