Question

Suppose that for a very large shipment of​ integrated-circuit chips, the probability of failure for any one chip is 0.10.Assuming that the assumptions underlying the binomial distributions are​ met, find the probability that at most 2 chips fail in a random sample of 19.

Answer 1

Solution

Given that ,

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X 2) = P(x = 0) + P(x = 1) + P(x = 2)

= (₁₉ C ₀) * 0.10⁰ * (0.90)¹⁹ + (₁₉ C ₁) * 0.10¹ * (0.90)¹⁸+ (₁₉ C ₂) * 0.10² * (0.90)¹⁷

= 0.7054

Probability = 0.7054