# Question: due to a mistake in the production line a box...

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Due to a mistake in the production line, a box of 100 calculators will always contain 20 calculators that are defective. Freddie and Brian each have a box of 100 calculators. Freddie will keep on selecting a calculator until he finds a defective calculator. On the other hand, Brian will select 5 calculators and will determine the number of defective calculators. Both of them will randomly select a calculator with replacement.

a. ) Find the probability that Freddie will select at most 4 calculators before he finds a defective calculator.

b. Find the expected number of calculators that Freddie will choose in order to select a defective calculator.

c. What is the probability that Brian will choose at most 1 defective calculator?

d. Find the expected number of defective calculators that Brian will choose.