Question

You study for an exam, but due to the fact that you waited too long, you only learn 60% of the material. The exam is all multiple choice, with each question having 5 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?
c) What is the overall probability of getting any question correct?

Answer 1

Answer: a)
`(1)/(2)`

b)
`(1)/(3)`

c)
`(1)/(6)`

Explanation:

The probability of a question from the material that was read = 60 % = 0.6

The probability of a question from the material that was not read = 40 % = 0.4

The probability of a right answer out of 5 questions
`=(1)/(5) = 0.2`

While, the probability of wrong answer = 1 - 0.2 = 0.8

a) Thus, by the definition of conditional probability,

The probability of getting a right answer when it is given that it is from the unread material
`=(0.2)/(0.4)=(1)/(2)`

b) The probability of getting a right answer when it is given that it is from the read material
`=(0.2)/(0.6)=(1)/(3)`

c) And, overall probability of a correct answer

= The correct answer is from the read material or the correct answer is from the unread material

=
`(1)/(2)* (1)/(3)= (1)/(6)`

Answer 2

a} The probability of getting a write answer of a question which you don't know the answer is 0.40*0.20 =0.08 or 8%.
b} The probability of getting a write answer of a question which you know the answer is 0.6*0.20=0.12 or 12%.
c) The probability of getting a write answer is 0.20 or 20%.