Binomial probability

[GDC]

A plan for reorganizing a corporation must be approved by 80% of the directors. If 15 directors are on the board, and if the probability that any of them will aprrove the reorganization is .7, find the probability of the plan being approved by the board. What assumptions are necessary for you to reach your conclusion.

[Adrian]

This is a binomial probability with total number n=15, probability of events (approval) p=0.7

The number of events occurring X >= 15*0.8 = 12,
P(X>=12)=P(X=12)+...+P(X=15)
probabilities can be obtained from the binomail table

Assumptions:
Each director must make decision independently.
There are fixed number of directors.
Probabilities of approval must remain constant for each director.