Given:

P (X = 1) = P (X = 2) = α

P (X= 4)=?

P(x=r)= ⁿC_r p^r q^n-r

P(x=1)= ⁿC₁ p¹ q^n-1

=npq^{n-1 (1)}

P(x=2)= ⁿC₂ p² q^n-2

⁽²⁾

Equating both equations ,we have:

2q = (n-1) p

4q² = (n-1)² p²

P(x=4)= ⁿC₄ p⁴ q^n-4

For large n; n

0

So,