Test Index

NCERT Class XII Mathematics Chapter - - Solutions

© examsnet.com
Question : 39
Total: 101
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let
3
4
 be the probability that he knows the answer and
1
4
 be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability
1
4
 .What is the probability that the student knows the answer given that he answered it correctly ?
Solution:  
Let E1 : ‘the student knows the answer’ and E2 : ‘the student guesses the answer’
⇒P(E1)=
3
4
 and P(E2)=
1
4

Let A : ‘the answer is correct’, then P(A|E1)=1 and P(A|E2)=
1
4
 (∵ when the student knows the answer, it is a sure event that the answer is correct) Hence, the required probability
=P(E1|A) =
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)

=
1×
3
4
(1×
3
4
)(
1
4
×
1
4
)
=
12
13
© examsnet.com
Go to Question:
Prev Question
Next Question