Hypergeometric, Poisson, and Geometric Distributions — Engineering Board Exam Practice Questions

6 free engineering board exam reviewer questions on Hypergeometric, Poisson, and Geometric Distributions (Combinatorics and Probability), each with the correct answer and a worked solution.

1. A box has 8 good and 4 defective items. Five items are drawn without replacement. What is the probability that at most 1 is defective?
2. Customers arrive at an average rate of 4 per hour (Poisson). What is the probability of at most 2 arrivals in one hour?
3. A shooter hits a target with probability 0.2 on each independent trial. What is the probability that the first hit occurs on the 4th trial?
4. A cable has an average of 2 defects per 10 meters (Poisson). What is the probability of no defects in a 10-meter length?
5. Calls arrive at a switchboard at an average rate of 3 per minute (Poisson). What is the probability of exactly 2 calls in a given minute?
6. A lot of 20 items contains 5 defective ones. Four items are sampled without replacement. What is the probability that exactly 1 is…