2. A vase contains 8 purple balls and 4 yellow balls. Three balls are taken out of the vase on a random basis without replacement. What is the probability that all three balls selected are yellow?

3. A recent report said that 40% of all California adults have a passport. Three California adults are selected at random. What is the probability that all three have a passport? (Since they are selected at random, and the population of California is huge compared to the sample size of 3, you can assume that whether one has a passport is independent of whether another has a passport.)

4. A club with 50 members is going to elect a president, a vice president, a secretary, and a treasurer. Assuming that no person can be elected to more than one office, in how many ways can the selection be made?

5. A clinic uses a diagnostic test to detect a certain disease. 2.5% (0.025) of all the patients at the clinic test positive, but just 0.4% (0.004) both test positive and actually have the disease. Given that a person tests positive what is the probability that they actually have the disease?

6. A restaurant offers five entrees, three vegetables, six beverages and five desserts. Assuming that a person orders one item of each type, in how many different ways can the person order a meal?

7. Assume that the probability that a California adult speaks English is 0.95, the probability that a California adult speaks Spanish is 0.10, and the probability that a California adult speaks English and Spanish is 0.095.

7.a What is the probability that a California adult either speaks English, or speaks Spanish, or both?

7.b Are speaking English or speaking Spanish independent events? To get full credit, show your work.

8. The following drawing represents a circuit. Either A must work correctly or B must work correctly for the system to operate. What is the probability that the system works correctly?

Device A

Probability of success = 0.98

Device B

Probability of success = 0.97

9. Assume that the probability that an American woman has children during her lifetime is 80%. Also assume that the probability that an American woman who has children gets breast cancer during her lifetime is 0.08, while the probability that any randomly selected American woman gets breast cancer is 0.11.

9.a What is the probability that an American woman both has children and experiences breast cancer during her lifetime?

9.bAre having children and having breast cancer independent events?