VITEEE 2015 Paper

Here, mean = 4 and variance = 2
⇒ np = 4 and npq = 2
So ,

npq

np

=

2

4

⇒ q =

1

2

Then, p = 1 - q = 1 -

1

2

=

1

2

Mean = np = 4
⇒ n ×

1

2

= 4 ⇒ n = 8
∴ P (X = r) =

n

‌

Crprqn−r
=

8

‌

Cr(

1

2

)8 [Since p = q =

1

2

]
The required probability of atleast 7 successes is
P (X ≥ 7) = P (X = 7) + P (X = 8)
= (

8

‌

C7+

8

‌

C8) (

1

2

)8
= (

8!

7!1!

+

8!

8!0!

) (

1

2

)8
= (8 + 1) (

1

2

)8 =

9

256