Chapter 4

1. A medical laboratory tests blood dor the presence of antibodies to the AIDS virus. For each blood specimen the outcome is “Yes” or “No.” Give a sample space for the results of the next 3 specimens tested.

2. The laboratory tests 800 blood specimens in a week, and counts the number of positive (“Yes”) results. This number varies randomly from week to week. Give a sample space for the weekly count of positive AIDS test results.

3. The table below gives two probability models. The left column gives the probabilities that a male worker chosen at random has each of several types of occupation. The right column gives the probability model for the occupation of a female worker chosen at random. Show that one of these is a legitimate probability model and the other is not.

	Male	Female
Occupation	Probability	Probability
Professional	0.28	0.28
Sales, etc	0.20	0.44
Service	0.08	0.16
Production	0.21	0.03
Operators	0.19	0.09

4. Consider the probability model for the occupation of female workers in Question #3.

a. What is the probability that a randomly selected female worker is a sales worker or a service worker?

b. What is the probability that she is not a production worker?

5. A difficult probability calculation shows that when a balanced coin is tossed 10 times, the probability that three straight heads appear somewhere in the 10 tosses is 0.508. The probability of seeing 3 straight tails is also 0.508.

6. a. To find the probability of seeing 3 dtraight heads or 3 straight tails in 10 tosses, we might add the probabilities of the two events,

P(A or B) = P(A) + P(B)

= 0.508 + 0.508

= 1.016

Why do you know that this result is wrong?

b. Explain why the addition rule for the probability that one or the other of the two separate events

occurs does not apply in this case.

7. A plant breeder is producing hybrid tomato plants. Each offspring from a particular cross has a probability ¾ of being fusarium-resistant and probability ½ of being tender-fruited. Inheritance of these characteristics is independent.

a. What is the probability that a plant is both fusarium-resistant and tender-fruited?

b. What is the probability that a plant is neither fusarium-resistant nor tender-fruited?

8. Sarah and Erin are among eight young executives competing for promotion to two managerial positions in their firm. Both Sarah and Erin have worked in marketing, while other candidates have backgrounds in finance or sales. Let A be the event that Sarah wins one of the positions and B be the event that Erin is one of those chosen. Are the events A and B disjoint? Is it reasonable to assume that they are independent?

9. Is each of the following random variable best described as discrete or continuous?

a. A technician examines a drop of blood under a microscope and counts the number X of red blood cells in a fixed area marked on the slide.

b. Another specimen of blood is analyzed chemically to report the level Y of triglycerides in milligrams per deciliter of blood.

10. A health maintenance organization (HMO) offers an unlimited number of visits to its member physicians for a fixed annual medical insurance payment. As part of its planning, the HMO records the number of office visits made in January to its physicians by each of the 120,000 people it covers. The distribution of the count X of visits is as follows.

Count	0	1	2	3	4	5	6	7
Probability	.25	.23	.18	.16	.08	.04	.03	.03

Display the distribution of X in a probability histogram. Then find the mean and standard deviation of X.