wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In a test an examinee either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 & the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it, is 1/8. Find the probability that he knew the answer to the question given that he correctly answered it.
If expressed in the form of a/b (simplest form), ba=?

Open in App
Solution

Let define the following events:
E1: Examine guesses the answer to the question.
E2: Examine copies the answer to the question.
E3: Examine know the answer to the question.
E: answer is correct
Here P(E1)=13,P(E2)=16
P(E3)=1(13+16)=12
Since the question is a multiple choice question with four choice so the probability that the answer is correct
when is guessed is P(EE1)=14
Also the probability that his answer is correct, given that he copied it is 18
i.e P(EE2)=18
Moreover his answer is correct, given he knew the answer is a sure event, so P(EE3)=1
Hence by Baye's theorem the required probability is
P(E3E)=P(EE3).P(E3)3i=1P(EEi).P(Ei)=1.1214.13+18.16+12.1=2429

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Bayes Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon