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Question

The probability that a stapler is broken is 0.2. If 10 staplers are randomly selected in a large office, find the probability that no more than 1 is defective.

Answer 1

The probability that none are defective is (0.8)^10.
P(d = 0) = (probability all 10 are good = 0.8^10)

The probability that exactly one is defective is (0.2)(0.8)^9 *10.
P(d = 1) = (probability 1 is bad and 9 are good * 10 ways (10C1 ways) to pick the defective stapler).

Add these together:
P(d = 0) = 0.8^10 = 0.107374182
P(d = 1) = (0.2)(0.8)^9 * 10 = 0.268435456

P(d <= 1) = 0.375809638
≈37.6%