Probability: 5 Problems and Solutions

1. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces:
a. Exactly 5 will be defective?
b. 5 or more will be defective?

2. Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that:
a. None of the antennas is defective.
b. Three or more of the antennas are defective.

3. Given: P(A1)=.20, P(A2)=.40, and P(A3)=.40. P(B1|A1)= .25 P(B1|A2)=.05, and P(B1|A3) =.10.

Use Bayes' theorem to determine P(A3|B1).

4. Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90 percent will pass the course. Among those students who do not do their homework, 60 percent will pass. Mike Fishbaugh took statistics last semester from Dr. Stallter and received a passing grade. What is the probability that he completed the assignments?

5. One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If a garage is robbed, what is the probability the doors were left open?