1. One design for a system requires the installation of two identical components. The system will work if at least one of the components works. An alternative design requires four of these components, and the system will work if at least two of the four components work. If the probability that a component works is 0.9, and if the components function independently, which design has the greater probability of functioning?
2. (Requires material from Section 3.3.) Refer to Example 4.14. Estimate the probability that exactly one of the four tires has a flaw, and find the uncertainty in the estimate.
3. If p is a success probability, the quantity p/(1 − p) is called the odds. Odds are commonly estimated in medical research. The article “A Study of Twelve Southern California Communities with Differing Levels and Types of Air Pollution” (J. Peters, E. Avol, et al., The American Journal of Respiratory and Critical Care Medicine, 1999:760–767) reports an assessment of respiratory health of southern California children. Assume that 88 boys in a sample of 612 reported being diagnosed with bronchitis during the last 12 months.
a. Estimate the proportion p of boys who have been diagnosed with bronchitis, and find the uncertainty in the estimate.
b. (Requires material from Section 3.3.) Estimate the odds, and find the uncertainty in the estimate.
