UPSC NDA I 2015 Mathematics Solved Paper

The target can be shot in the following ways:
Either ‘A’ hits and B does not hit or B hits A does not hit, or both of them hit the target or none of them hit the target.
Now it is given that exactly one of them hits the target. Therefore the last two cases are ruled out. Hence we are left with Either ‘A’ hits and B does not hit or B hits A does not hit.
Therefore, the required probability will be
P(A).P(B′)+P(A′)P(B)
=(

1

2

)(1−

1

3

)+(1−

1

2

)(

1

3

)
=(

1

2

)(

2

3

)+(

1

2

)(

1

3

)
=

1

3

+

1

6

=

3

6

=

1

2

=50%