Answered

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.

AIf you come across a question for which you don't know the answer, what's the probability of getting the answer right?
BIf you come across a question for which you do know the answer, what's the probability of getting it right?
CWhat is the overall probability of getting any question correct?

Verified Answer :

meerkat18

a} The probability of getting a write answer of a question which you don't know the answer is 0.400.20 =0.08 or 8%. 
b} The probability of getting a write answer of a question which you know the answer is 0.60.20=0.12 or 12%.
c) The probability of getting a write answer is 0.20 or 20%. 

Answer:  a) \(\frac{1}{2}\)

b)  \(\frac{1}{3}\)

c) \(\frac{1}{6}\)

Step-by-step 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  \(=\frac{1}{5} = 0.2\)

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 \(=\frac{0.2}{0.4}=\frac{1}{2}\)

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

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

= \(\frac{1}{2}\times \frac{1}{3}= \frac{1}{6}\)

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