1. A tire manufacturer has started a program to monitor production. In every batch of eight tires, two will be randomly selected and electronically tested for defects. An experiment consists of recording the condition of these two tires: defect-free (G) or reject (B). Suppose two of the eight tires in a batch actually contain serious defects.
2. a. List the outcomes in this experiment
3. b. What is the probability that both tires selected will be defect free?
4. c. What is the probability that at least one of the tires selected will contain a defect?
5. d. What is the probability that both tires selected will contain a defect?

2. According to the Census Bureau, in 2000, 86.9% of the adults in the United States aged 65 or older were Caucasian and 8.1% were African American. Two percent of those 65 or older are Caucasian and have had difficulty obtaining health care and 0.3% of those 65 or older are African American and have had difficulty obtaining health care (Source: U.S. Census Bureau, Census 2000 and Medicare Current Beneficiary Survey). Suppose an adult 65 or older is selected at random.

a. Suppose the adult is Caucasian, what is the probability the adult had difficulty obtaining health care?

b. Suppose the adult is African American, what is the probability the adult had difficulty obtaining health care?

c. Suppose the adult is African American, what is the probability the adult had no difficulty obtaining health care?

d. Suppose the adult had difficulty obtaining health care, what is the probability the adult is Caucasian? African American?

3. Suppose that Saint Christopher's Hospital in Philadelphia has three emergency generators for use in case of a power failure. Each generator operates independently, and the manufacturer claims that the probability each generator will function properly during a power failure is 0.95.

a. What are the possible outcomes in case of a power failure?

b. Construct the probability distribution for these outcomes letting X be the number of failures.

c. Suppose a power failure occurs and all three generators fail. Is there reason to doubt the manufacturers claim?

4. A new pharmaceutical agent has been developed for the treatment of certain symptoms caused by asthma. Based on a clinical trial, the manufacturer claims only 10% of patients at least 12 years of age using this medication will experience tachycardia or rapid heart rate as an adverse reaction to the drug. Suppose 30 people (at least 12 years old) who need this medication are selected at random. Each volunteer is given the new drug and the number of people who experience tachycardia is recorded.

1. What is the probability that at most one person will experience tachycardia?
2. Suppose seven people experienced tachycardia. Does this suggest that the companies claim is incorrect? Why or why not?

5. It is estimated that 14% of all drivers in Pennsylvania are uninsured. Suppose the Pennsylvania State Police establish a checkpoint and randomly stop cars to inspect the driver's license, registration, and proof of insurance.

1. What is the probability the third person stopped will be the first uninsured driver?
2. What is the probability it will take at least five cars before the 1st uninsured driver is detected?