UPSC NDA Math Model Paper 1

Given:
Urn 1: 1 black and 1 green ball
Total ball in urn 1 = 2 balls
Urn 2: 1 white and 1 green ball
Total ball in urn 1 = 2 balls
One ball is drawn from each,
So total balls are drawn two.
To find: The probability of getting at least one green ball
Possible ways:
if we get 1 green from urn 1 and 1 white from the urn 2
if we get 1 green from urn 2 and 1 black from the urn 1
if we get 1 green from urn 1 and 1 green from the urn 2
Hence, the probability that both balls are of the same colour = P(G1)×P(W2)+P(G2)×P(B1) +P(G1)×P(G2)
=

1

2

×

1

2

+

1

2

×

1

2

+

1

2

×

1

2

=

1

4

+

1

4

+

1

4

=

3

4