Question 1. Determine whether the situation proposed is a relative frequency definition or a subjective definition.
Potential investors for a new housing community would like an estimate for the probability that 80% of the lots will be sold by the end of the first six months of sales.
Subjective definition
Relative frequency definition
Question 2. Provide an appropriate response.
Both parents are carriers for an inheritable trait so that the probability their child possesses the trait is 25%. Given that the couple has 4 children, which of the following is true?
At least two of the children must possess the trait
Exactly one of the children must possess the trait
It is possible that none of the four children possess the trait
It is impossible that all four children possess the trait
Question 3. Determine whether the situation proposed is a relative frequency definition or a subjective definition.
A travel agent calculates the probability that an airline will be on time for a given flight by looking at their flight records for that city pair over the past two years.
Relative frequency definition
Subjective definition
Question 4. Answer true or false.
Two trials are independent if they have no outcomes in common.
False
True
Question 5. Determine whether the situation proposed is a relative frequency definition or a subjective definition.
If both parents are carriers for Tay-Sachs, the probability that their child will have Tay-Sachs is 25%.
Relative frequency definition
Subjective definition
Question 6. Answer true or false.
If you roll a die 50 times, you are guaranteed to see each of the six faces at least once.
False
True
Question 7. Provide an appropriate response.
You play a game where you are to guess under which of 4 cups a coin has been placed. How many times would you expect to guess correctly in 20 plays of the game? Note that the coin is moved after each play.
10
4
1
5
Question 8. Determine whether the events are disjoint.
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 2890
21-24 2190
25-28 1276
29-32 651
33-36 274
37-40 117
Over 40 185
A student from the community college is selected at random. The events A, B, and C are defined as follows.
A = event the student is at most 28
B = event the student is at least 40
C = event the student is between 21 and 24 inclusive
Are the events A, B, and C disjoint?
a. Yes
b. No
Question 9. Suppose P(C) =0 .048, P(M and C) = 0.044, and P(M or C) = 0.524. Find the indicated probability.
P(M)
0.524
0.528
0.480
0.520
0.472
Question 10. Find the indicated probability.
According to a survey, 59% of teens have family dinners five or more times a week, 13% of teens have used marijuana and the proportion of teens who have family dinners 5 or more times a week or use marijuana is 0.64. What is the probability that a teen has family dinners five or more times a week and uses marijuana?
cannot be determined from the information given
0.08
0.18
0.64
0.077
Question 11. Provide an appropriate response.
According to a survey, 41.5% of babies born in the U.S. were still being breastfed at 6 months of age. If 4 children who are born in the U.S. are randomly selected, what is the probability that none of them are breastfed for at least 6 months?
1
0.03
none of these
0.585
0.12
Question 12. Find the indicated probability.
The probability that a student at a certain college is male is 0.45. The probability that a student at that college has a job off campus is 0.33. The probability that a student at the college is male and has a job off campus is 0.15. If a student is chosen at random from the college, what is the probability that the student is male or has an off campus job?
0.47
0.78
0.37
0.63
0.93
Question 13. Determine whether the events are disjoint.
The number of hours sixth grade students took to complete a research project was recorded with the following results.
Hours Number of students (f)
4 15
5 11
6 19
7 6
8 9
9 16
10 2
A student is selected at random. The events A and B are defined as follows.
A = event the student took at most 9 hours
B = event the student took at least 9 hours
Are the events A and B disjoint?
Yes
No
Question 14. Find the indicated probability.
88.2% of respondents to a survey answered "yes" when asked if it should be possible for a pregnant woman to obtain a legal abortion if the woman's own health was seriously endangered by the pregnancy and 91.4% answered "yes" when asked whether they were in favor of sex education in public schools. If 82.6% of the respondents answered "yes" to both questions, what is the probability that a randomly selected respondent answered "yes" to at least one of the questions?
0.97
0.914
0.794
1
0.858
Question 15. Provide an appropriate response.
Identify the sample space for the following probability experiment: recording the number of days it snowed in Cleveland in the month of January.
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . . . , 30, 31}
{0, 1, 2, 3, . . ., 12}
{0, 1}
{30, 21}
{0, 1, 2, 3}
Question 16. Find the indicated probability.
A group of volunteers for a clinical trial consists of 83 women and 78 men. 21 of the women and 20 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person is a man given that they have high blood pressure.
0.256
0.512
0.488
0.124
0.255
Question 17. Find the indicated probability.
A survey asked 1963 respondents whether they favored or opposed a gun law requiring people to have a permit in order to purchase a gun. The responses, categorized by gender, are given in the table below.
Given that a respondent favors the gun law, what is the probability that they are female?
0.45
0.61
0.88
0.49
0.86
Question 18. Provide an appropriate response.
A survey asked respondents whether they favored or opposed sex education in public schools. According to the survey results, 44% of the respondents were male and 89% favored sex education in public schools. The probability that a respondent is male and favors sex education in public schools is 39%. Are the events "respondent is male" and "respondent favors sex education in public schools" independent?
No, because P(A and B) = P(A)P(B)
Yes, because P(A and B) ≠ 0
Yes, because P(A and B) = P(A)P(B)
No, because P(A or B) ≠ P(A)
Question 19. Find the indicated probability.
A group of volunteers for a clinical trial consists of 81 women and 77 men. 18 of the women and 19 of the men have high blood pressure. If one of the volunteers is selected at random find the probability that the person has high blood pressure given that it is a woman.
0.486
0.234
0.356
0.114
0.222
Question 20. Solve the problem.
A patient is told that a test for a certain disease is 92% accurate. The way this is worded, this could mean that (a) 92% of those with the disease test positive, (b) 92% of those without the disease test negative, (c) 92% of those who test positive have the disease, or (d) 92% of those who test negative do not have the disease. Let D denote {person has the disease}, and let P denote {person tests positive}. Using these events and their complements, express as a conditional probability the event that a person without the disease tests negative.
P( Dc)
P( Dc)
P( P)
P( D)
P( Pc)
Question 21. Provide an appropriate response.
Mr. Smith's gardener is not dependable; the probability that he will forget to water the rosebush during Smith's absence is 2/3. The rosebush is in questionable condition anyhow; if watered, the probability of its withering is 1/2, but if it is not watered, the probability of its withering is 3/4. Upon returning, Smith finds that the rosebush has withered. What is the probability that the gardener did not water the rosebush?
None of these.
Question 22. Provide an appropriate response.
An online clothing store carries three brands of jeans. 40% of their jean sales are brand A, 20% are brand B and the remainder are brand C. 20% of brand A's jeans cost over $100, 40% of brand B's jeans cost over $100 and 90% of brand C's jeans cost over $100. Given that a pair of jeans is purchased for over $100, what is the probability that they are brand A?
0.154
0.148
0.08
0.4
0.133
Question 23. Provide an appropriate response.
Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of its contents defective, while shipment II has 5% of its contents defective. Given that a randomly selected component is defective, what is the probability it came from shipment II? Assume that it is equally likely that the component came from shipment I as from shipment II.
0.384
0.714
0.286
0.5
0.2