Suppose just twothirds of all voters support a certain propo

Suppose just two-thirds of all voters support a certain proposition. 800 voters are chosen at random. Find the probability that a majority of these 800 oppose the proposition.

Solution

p = 2/3

No of voters = 800

As each voter is independent, and there are two outcomes, X- no of voters is Binomial with (800, 2/3)

P(a majority of these 800 oppose the proposition.) = P(x<400)

= 7.845x10^-23