Question

A high-security government installation has installed 4 security systems to detect attempted break-ins. The 4 security systems operate independently of each other, and each has a .40 probability of detecting an attempted break-in. Assume an attempted break-in occurs. Use the binomial distribution to find the probability that at least one of the 4 security systems will detect it. (Round your answer to 4 decimal places.)

Probability

Answer 1

Here, n = 4, p = 0.4, (1 - p) = 0.6 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) = (4C1 * 0.4^1 * 0.6^3) + (4C2 * 0.4^2 * 0.6^2) + (4C3 * 0.4^3 * 0.6^1) + (4C4 * 0.4^4 * 0.6^0)
P(X >= 1) = 0.3456 + 0.3456 + 0.1536 + 0.0256
P(X >= 1) = 0.8704