CGPET 2021 Solved Paper

P(A)=Probability of solving a problem by A+

1

2

P(B) = Probability of solving a problem by B=

1

3

P(C) = Probability of solving a problem by C+

1

4

∵ A, B and C are independent events.
⇒ P(A∩B∩C)=P(A).P(B).P(C)
=

1

2

.

1

3

.

1

4

=

1

24

⇒ Probability that problem is solved
=P(A∪B∪C)
1−P

−

(A∪B∪C)

=1−P(

−

A

∩

−

B

∩

−

C

)
=1−P(

−

A

).P(

−

B

).P(

−

C

)
=1−(1−P(A)(1−P(B)(1−P(C))
=1−(1−

1

2

)(1−

1

3

)(1−

1

4

)
=1−(

1

2

)(

2

3

)(

3

4

)
=1−

1

4

=

3

4