AP EAMCET Engineering 2012 Solved Paper

Let E1: The event that the students knows the answer and
E2: The event that the student guesses the answer
∴P(E1)=

9

10

and P(E2)=1−

9

10

=

1

10

Let E: The answer is correct.
The probability that the student answered correctly, given that he knows the answer
i.e., P(

E

E1

)=1
The probability that the students answered correctly, given that he guessed is

1

4

.
i.e., P(

E

E2

)=

1

4

By using Baye's theorem,
P(

E2

E

) =

P( E E2 )P(E2)

P( E E1 )P(E1)+P( E E2 )P(E2)

=

1 4 × 1 10

1× 9 10 + 1 4 × 1 10

=

1 40

9 10 + 1 40

=

1 40

36+1 40

=

1

37