JEE Advanced Model Paper 8 with solutions for online practice

Let E1 = Event that A wrote a plus sign .
E2 = Event that A wrote aminus sign .
E = Event that the referce observes a plus sign.
Given , P (E1) =

1

2

⇒ P (E2) =

2

3

P (E/E1) = Probability that none of B,C,D change sign+Probability that exactly two of
B , C , D Change sign.
=

1

27

+ 3 (

1

3

×

2

3

×

2

3

) =

13

27

P (E/E2) = Probability that all of B,C,D change the sign+Probability that exactly one of themchanges the sign.
=

8

27

+ 3 × (

2

3

×

1

3

×

1

3

) =

14

27

∴ P (E1/E) =

13

41

Using Baye’s theorem.