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It is known that 10% of the items produced by a certain machine end up having a flaw. If we select 7 items from the production line, a) What is the probability that at least one of them has a flaw? Part b) What is the probability that exactly three of them has a flaw?

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MathPhys

Step-by-step explanation:

p = 0.1, q = 0.9, n = 7

a) Use complementary probability.

P(at least 1) = 1 − P(0)

P(at least 1) = 1 − (0.9)⁷

P(at least 1) = 0.522

b) Use binomial probability.

P = nCr pʳ qⁿ⁻ʳ

P(3) = ₇C₃ (0.1)³ (0.9)⁴

P(3) = 0.023

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