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MHT CET 2021 Math Solved Paper
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© examsnet.com
Question : 62
Total: 100
A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is
p
,
0
<
p
<
1
. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is
3
p
4
p
+
3
5
p
3
p
+
2
5
p
4
p
+
1
4
p
3
p
+
1
Validate
Solution:
Let
E
1
=
Student does not know the answer
E
2
=
Student knows the answer
and
E
=
student answer correctly
∴
P
(
E
1
)
=
1
−
p
⇒
P
(
E
2
)
=
p
⇒
P
(
E
E
2
)
=
1
and
P
(
E
E
1
)
=
1
5
Note that, the probability that student did not know the answer randomly
=
The probability that student know the answer.
∴
P
(
E
2
E
)
=
P
(
E
2
)
P
(
E
E
2
)
P
(
E
1
)
P
(
E
E
1
)
+
P
(
E
2
)
P
(
E
E
2
)
=
p
(
1
)
(
1
−
p
)
1
5
+
p
(
1
)
=
p
1
−
p
+
5
p
5
=
5
p
1
+
4
p
© examsnet.com
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