UPSC NDA Math Model Paper 2

It is given that P(A) =

1

2

and P(not B) =

1

4

. Let's say that the probability of C solving the problem is P(C) = x.
∴ Probability of A not solving the problem =P(notA)=1−P(A)=1−

1

2

=

1

2

.
And, probability of C not solving the problem = P(not C) = 1 - P(C) = 1 - x.
Now, the probability that the problem is not solved at all:
= P(not A) AND P(not B) AND P(not C)
= P(not A) × P(not B) × P(not C)
=

1

2

×

1

4

×(1−x)
=

1−x

8

And, the probability that the problem is solved = 1 - Probability that the problem is not solved at all =

63

64.

⇒1−

1−x

8

=

63

64

⇒

1−x

8

=1−

63

64

=

1

64

⇒1−x=

1

8

⇒x=1−

1

8

=

7

8

∴ The probability of C solving the problem is P(C)=x=

7

8