UPSC NDA I 2019 Mathematics Solved Paper

(B)
Since A and B are independent events P( A∩ B) = P( A). P(B)
⇒ P( A) .P(B) =

1

6

….(i)
Now P( A ∪ B) =

2

3

⇒ P( A) + P(B) − P( A∩ B) =

2

3

⇒ P( A) + P(B) −

1

6

=

2

3

⇒ P( A)+P(B) =

5

6

…(ii)
From (i) and (ii)
P(B) =

1

3

,

1

2

⇒ P(B) = 1/3 ( given P(B) < P( B) < P(A) )