Question

A candidate for public office is thought to have support from 65% of the voters. A
random sample of six voters is taken. What is the probability that there will be at least four who
support the candidate?

Answer 1

Here, n = 6, p = 0.65, (1 - p) = 0.35 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 4).
P(X >= 4) = (6C4 * 0.65^4 * 0.35^2) + (6C5 * 0.65^5 * 0.35^1) + (6C6 * 0.65^6 * 0.35^0)
P(X >= 4) = 0.328 + 0.2437 + 0.0754
P(X >= 4) = 0.6471