1- Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2-3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2-3 subsystem.

The experiment consists of determining the condition of each component [S(success) for a functioning component andF(failure) for a nonfunctioning component].

- Which outcomes are contained in the eventAthat exactly two of the three components function?

- Which outcomes are contained in the eventCthat the system functions?

- List outcomes inAC.

2- Suppose that50% of all adults regularly consume coffee,60% regularly consume carbonated soda, and75% regularly consume at least one of these two products.

- What is the probability that a randomly selected adult regularly consumes both coffee and soda?

- What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

3- An insurance company offers four different deductible levelsnone, low, medium, and highfor its homeowner's policyholders and three different levelslow, medium, and highfor its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.05(5%of all such individuals).

Homeowner's Auto N L M H L 0.04 0.05 0.05 0.02 M 0.07 0.08 0.20 0.14 H 0.02 0.03 0.15 0.15

Suppose an individual having both types of policies is randomly selected.

- What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?

- What is the probability that the individual is in the same category for both auto and homeowner's deductibles?

- What is the probability that the individual has at least one low deductible level?

4-Suppose that the proportions of blood phenotypes in a particular population are as follows:

A B AB O 0.50 0.07 0.03 0.40

- Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O?

- What is the probability that the phenotypes of two randomly selected individuals match?

5- An aircraft seam requires 30rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability.

If 17% of all seams need reworking, what is the probability that a rivet is defective?