ES9 Additional Exercises

Chapter 4

1. An article titled "Pain and Pain-Related Side Effects in an ICU and on a Surgical Unit: Nurses' Management" (American Journal of Critical Care, January 1994, Vol. 3, No. 1) gave the following table summarizing the study participants. (Note: ICU is an acronym for intensive care unit.)

Gender ICU Surgical Unit

Female 9 6

Male 11 18

One of these participants is randomly selected. Answer the following questions.

a. Are the events "being a female" and "being in the ICU" mutually exclusive?

b. Are the events "being in the ICU" and "being in the surgical unit" mutually exclusive?

c. Find P(ICU or female).

2. 
   Find P(ICU or male).
   

2. Tracy Shark walked into the card room at her country club and played one hand of bridge at one table and one hand of poker at another table. She was dealt a bridge hand with all 13 cards in the same suit, and then she was dealt a poker hand with a royal flush. As she left the room shaking her head, she was overheard mumbling, “I doubt that will happen again in a million years.” Assuming the decks were shuffled and the dealers were straight, compute the probability of the joint occurrence of the two events. Do you agree with Tracy?

3. The December 1994 issue of The American Spectator quotes a poll by the Times-Mirror Center for the People and the Press as finding that 71% of Americans believe that the press "gets in the way of society solving its problems."

a. If two Americans are randomly selected, find the probability that both will believe that the press "gets in the way of society solving its problems."

b. If two Americans are selected, find the probability that neither of the two will believe that the press "gets in the way of society solving its problems."

c. If three are selected, what is the probability that all three believe the press gets in the way?

4. The August 1, 1994, issue of The New Republic gives the results of a U.S. Justice Department study which states that among white spousal murder victims, 62% are female. If the records of three victims are randomly selected from a large data base of such murder victims, what is the probability that all three victims are male?

5. An article involving smoking cessation intervention in Heart & Lung (March/April 1994, Vol. 23, No. 2) divided 80 subjects into a two-way classification:

Experimental 10 14 13

Usual Care 12 16 15

Suppose one of these 80 subjects is selected at random. Find the probabilities of the following events.

a. The subject is not in the experimental group.

b. The subject is in the experimental group and has oncology diagnosis.

c. The subject is in the experimental group or ha a cardiovascular diagnosis.

6. A study concerning coping strategies of abstainers from alcohol appeared in Image, the Journal of Nursing Scholarship (Vol. 25, No. 1, Spring 1993). The study involved 23 subjects who were classified according to sex as well as marital status as shown in the table.

Marital Status Men Women

Currently married 10 3

Divorced/separated 3 6

Never married 1 0

One of the subjects is selected at random. Find:

a. The probability the subject is currently married given that the individual is a man.

b. The probability the subject is a woman given that the individual is divorced/separated.

3. 
   The probability the subject is a man given that the individual has never married.
   

7. An article titled "A Puzzling Plague" found in the January 14, 1991, issue of Time, stated that one out of every ten American women will get breast cancer. It also states that of those who do, one out of four will die of it. Use these probabilities to find the probability that a randomly selected American woman will

a. never get breast cancer.

b. get breast cancer and not die of it.

3. 
   get breast cancer and die from it.
   

8. The Pennsylvania Lottery game big 4 has been played for more than 18 years. The table below lists the number of times each single-digit number was the winning number for each of the four positions. The frequencies for each number in each position range from 304 to 367.

Number	First	Second	Third	Fourth	Total
0	343	312	352	328	1335
1	326	330	351	357	1364
2	347	323	315	344	1329
3	320	327	350	351	1348
4	304	345	331	318	1298
5	321	348	322	343	1334
6	339	306	329	316	1290
7	348	346	351	311	1356
8	337	367	329	350	1383
9	360	341	315	327	1343

a. Do the frequencies of each number as a winner in the first position appear to indicate that the numbers occur randomly as first position winners? What statistical evidence can you find to justify your answer? Present a convincing case.

b. Do the frequencies of each number as a winner in the second, third and fourth positions appear to indicate that the numbers occur randomly as position winners? What statistical evidence can you find to justify your answer? Present a convincing case.

c. Each single-digit number has appeared as a winning number a different number of times ranging from 1290 to 1383. Do you think these numbers vary sufficiently to make a case that the digits do not occur with equal probability? Present evidence to support your answer.

9. According to the National Cancer Data Base report for Hodgkin's disease (CA-A Cancer Journal for Clinicians, Jan./Feb. 1991), the highest percentage of patients (31%) were 20 to 29 years of age, and they had a three-year observed survival rate of 91%. What is the probability that an individual who has been diagnosed with Hodgkin's disease is between 20 and 29 years of age and will survive for three years?