UPSC NDA I 2025 Mathematics Paper

Given,
The probability that A,B, and C become managers are:
P(A)=‌

3

10

,P(B)=‌

1

2

,P(C)=‌

4

5

The conditional probabilities that the bonus scheme is introduced are:
P(D∣A)=‌

4

9

,P(D∣B)=‌

2

9

,P(D∣C)=‌

1

3

The total probability that the bonus scheme will be introduced is given by:
P(D)=P(D∣A)P(A)+P(D∣B)P(B)+P(D∣C)P(C)
Substituting the values:
P(D)=(‌

4

9

×‌

3

10

)+(‌

2

9

×‌

1

2

)+(‌

1

3

×‌

4

5

)
Now, simplifying the terms:
P(D)=‌

12

90

+‌

2

18

+‌

4

15

The least common denominator (LCD) is 90. So:
P(D)=‌

12

90

+‌

10

90

+‌

24

90

Adding the fractions gives:
P(D)=‌

46

90

=‌

23

45