A manufacturing machine has a 3% defect rate. If 5 items are chosen at random, what is the probability that at least one will have a defect?

Question

Round your answer to 4 decimal places

Answer 1

At least one being defective:

Either some are bad or none are::

P(1 or more bad) + P(none) = 1

P(1 or more bad) = 1- P(none)

Independent measurements

P(none) = P(ok) P(ok) P(ok) P(ok) P(ok) = P(ok)^5

P(none) = (1 - 0.03)^5 = (0.97)^5 = 0.86 = 86%

P(1 or more bad) = 1- P(none) = 14%