UPSC NDA Math Model Paper 5

Let box A, box B and box C be the three boxes respectively.The given event is a Compound Event which can be written as:
[(1G from box A) and (1R from box B) and (1R from box C)]
or [(1R from box A) and (1G from box B) and (1R from box C)]
or [(1R from box A) and (1R from box B) and (1G from box C)]
∴P=(

‌1C1

‌4C1

×

‌2C1

‌4C1

×

‌1C1

‌4C1

)+(

‌3C1

4C1

×

‌2C1

‌PC1

×

‌1C1

‌PC1

) +(

‌3C1

‌4C1

×

‌2C1

‌4C1

×

‌3C1

‌4C1

)
⇒P=(

1

4

×

2

4

×

1

4

)+(

3

4

×

2

4

×

1

4

) +(

3

4

×

2

4

×

3

4

)
⇒P=

2

64

+

6

64

+

18

64

⇒P=

26

64

⇒P=

13

32