UPSC NDA Math Model Paper 3

Given: 16 P (X = 4) = P (X = 2)
To find the value of p
Calculating probabilities of random variable X,
P(X=4)=(

6

4

)p4(1−p)2
P(X=2)=(

6

2

)p2(1−p)4
Given,16 P (X = 4) = P (X = 2)
⇒16(

6

4

)p4(1−p)2 =(

6

2

)p2(1−p)4
⇒16×

6!

2!4!

p4(1−p)2 =

6!

2!4!

p2(1−p)4
⇒16p2=(1−p)2
⇒±4p=1−p
⇒p=

1

5

or p=−

1

3

Hence, p=

1

5