Question

An electronic system contains 10 cooling components that operate independently. The probability of each component's failure is 0.2. The system will overheat if and only if at least 3 components fail. Calculate the probability that system will overheat. (Hint: You might need to use the Binomial Table)

Answer 1

Here, n = 10, p = 0.2, (1 - p) = 0.8 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

P(X <= 2) = (10C0 * 0.2^0 * 0.8^10) + (10C1 * 0.2^1 * 0.8^9) + (10C2 * 0.2^2 * 0.8^8)
P(X <= 2) = 0.1074 + 0.2684 + 0.302
P(X <= 2) = 0.6778

P(X >= 3) = 1 - 0.6778 = 0.3222

Ans: 0.3222