You find a container of 30 old pens in your school supplies and continue to test

Question

You find a container of 30 old pens in your school supplies and continue to test them (without replacement), until you find one that works. If each individual pen works 22% of the time (regardless of the other pens), what is the probability that you find one that works within the first four tries?

First, what is the probability the first randomly selected pen works?

What is the probability the second pen is the first that works? (Round the answer to three decimals.)

What is the probability one of the first four tries works? (Round the answer to two decimals.)

Explanation / Answer

Probability of pen works = 0.22

Probability of doesn't work= 1 - 0.22 = 0.78

A) probability of first randomly selected pen works = 0.22

B) probability of second pen is the first that works = first doesn't work * second works = 0.78 * 0.22 = 0.17

C) probability of one of the first four tries works = 0.22 * 0.78 * 0.78 * 0.78 + 0.78 * 0.22 * 0.78 * 0.78 + 0.78 * 0.78 * 0.22 * 0.78 + 0.78 * 0.78 * 0.78 * 0.22 = 0.42

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