JEE Mains Model Paper 25

Let G, E1 , E2 , E denote the followign events:
G : Original signal is green
E1 : A receives the signal correctly
E2 : B receives the signal correctly
E : B receives the green signal
We have E = GE1E2 ∪ GE1′E2′ ∪ G′E1′E2′ ∪ G′E1′E2′
⇒ P(E) = P(GE1E2) + P(GE1′E2′) + P(G′E1E2′) + P(G′E1′E2′)

=

4

5

3

4

3

4

+

4

5

1

4

1

4

+

1

5

3

4

1

4

+

1

5

1

4

3

4

=

36+4+3+3

80

=

23

40

Also , P (G ∩ E) =

P(G∩E)

P(E)

=

1∕2

23∕40

=

20

23