Question

In Cape Town, South Africa 30% of workers drive to work. In a sample of 10 workers, what is the probability that at least 1 worker drives to work?

Answer 1

Here, n = 10, p = 0.3, (1 - p) = 0.7 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 1).
P(X >= 1) = (10C1 * 0.3^1 * 0.7^9) + (10C2 * 0.3^2 * 0.7^8) + (10C3 * 0.3^3 * 0.7^7) + (10C4 * 0.3^4 * 0.7^6) + (10C5 * 0.3^5 * 0.7^5) + (10C6 * 0.3^6 * 0.7^4) + (10C7 * 0.3^7 * 0.7^3) + (10C8 * 0.3^8 * 0.7^2) + (10C9 * 0.3^9 * 0.7^1) + (10C10 * 0.3^10 * 0.7^0)
P(X >= 1) = 0.1211 + 0.2335 + 0.2668 + 0.2001 + 0.1029 + 0.0368 + 0.009 + 0.0014 + 0.0001 + 0
P(X >= 1) = 0.9717