I am trying to understand a paper on options titled "OPTION PRICING: A SIMPLIFIED APPROACH". In it option price is calculated as the expected payoff from the possible states of stock prices by binomial distribution approach.

I am stuck at one step.

What does this exactly mean:

Now, the latter bracketed expression is the complementary binomial distribution function Φ[a; n,p]. The first bracketed expression can also be interpreted as a complementary binomial distribution function Φ[a; n, p’]

 Thank you in advance.

Citation :

OPTION PRICING: A SIMPLIFIED APPROACH

John C. COX

Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Stanford University, Stanford, CA 94305, USA

Stephen A. ROSS

Yale University, New Haven, CT06520, USA

Mark RUBINSTEIN

University of Califorma, Berkeley, CA 94720, USA

Journal of Financial Economics 7 (1979) 229-263. 0 North-Holland Publishing Company

I am trying to understand a paper on options titled "OPTION PRICING: A SIMPLIFIED APPROACH" [1]. In it option price is calculated as the expected payoff from the possible states of stock prices by binomial distribution approach.
I am stuck at one step.
What does the following sentences exactly mean?

Now, the latter bracketed expression is the complementary binomial distribution function $\Phi[a; n,p]$. The first bracketed expression can also be interpreted as a complementary binomial distribution function $\Phi[a; n, p’]$.

Thank you in advance.

Bibliography

[1] John C. COX and Stephen A. ROSS and Mark RUBINSTEIN "Option Pricing: A Simplified Approach", Journal of Financial Economics 7 (1979) 229-263. DOI: 10.1016/0304-405X(79)90015-1