Exercises
3.4.1:
In a study of the influence of social and political violence on the risk of pregnancy complications, a researcher collected extensive information collected on a sample of 161 pregnant women between the ages of 19 and 40 years who were enrolled for prenatal care in six health centers in Santiago. Chile. The following table shows the sample subjects cross-classified according to education level and number of pregnancy complications:
Number of Pregnancy Complications
___________________________________
Education(years) >=2 0-1 Total
___________________________________________________
1-3 23 53 75
4-8 9 23 32
9-10 10 27 37
>=11 5 12 17
___________________________________________________
Total 46 115 161
(a) Suppose we pick a woman at random from this group. What is the probability that this woman will be one with two or more pregnancy complications?
(b) What do we call the probability calculated in part a?
(c) Show how to calculate the probability asked for in part a by two additional methods.
(d) If we pick a woman at random, what is probability that she will one with two or more pregnancy complications and have 4-8 years of education?
(e) What do we call the probability calculated in part d?
(f) Suppose we pick a woman at random and fined that she has zero or one pregnancy complication. What is probability that she has 11 years or more of education?
(g) What do we call the probability calculated in part f?
(h) Suppose we pick a woman at random. What is the probability that she is one with two or more pregnancy complications or has less than 4 years of education or both?
(i) What do we call the method by which you obtained the probability in part h?
ANSWER
(a) 0.2857
(b) Marginal.
(c) 0.2857, 1-0.7143=0.2857
(d) 0.0559
(e) Joint
(f) 0.1043
(g) Conditional
(h) 0.6149
(i) Addition rule
3.4.5: If the probability of left-handedness in a certain group of people is 0.05, what is the probability of right-handedness (assuming no ambidexterity)?
ANSWER
0.95
3.4.6: The probability is .6 that a patient selected at random from the current residents of a certain hospital will be a male. The probability that the patient will be a male. The probability that the patient will be a male who is in for surgery is v.2. A patient randomly selected from current residents is found to be a male; what is the probability that the patient is in the hospital for surgery?
ANSWER
0.333
3.4.7: In a certain population of hospital patients the probability is .35 that a randomly selected patient will have heart disease. The probability is .86 that a patient with heart disease is a smoker. What is the probability that a patient randomly selected from the population will be a smoker and have heart disease?
ANSWER
0.301
REVIEW QUESTION AND EXERCISES
6: A certain county health department has received 25 applications for an opening that exists for a public health nurse. of thses applicants ten are over 30 and fifteen are under 30. Seventeen hold bachelor s degree only, and eight have master s degrees. Of those under 30, six have master s degrees. If a selection from among these 25 applicants is made at random, what is the probability that a person over 30 or a person with a master s degree will be selected?
ANSWER
0.64
8:If the probability that a public health nurse will find a client at home is .7, what is the probability (assuming independence) that on two home visits made in a day both clients will be home?
ANSWER
0.49
10: In a certain population the probability that a randomly selected subject will have been exposed to a certain allergen and experience a reaction to the allergen is .60. The probability is .8 that a subject exposed to the allergen will experience an allergic reaction . If a subject is selected at random from this population, what is the probability that he/she will have been exposed to the allergen?
ANSWER
0.75
11: Suppose that 3 percent of the people in a population of adults have attempted suicide. It is also known that 20 percent of the population are living below the poverty level. If these two events are independent, what is the probability that a person selected at random from the population will have attempted suicide and be living below the poverty level?
ANSWER
0.006
12: In a certain population of women 4 percent have had breast cancer, 20 percent are smokers, and 3 percent are smokers and have had breast cancer. A woman is selected at random from the population. What is the probability that she has had breast cancer or smokes or both?
ANSWER
0.21