Download College Prep Stats Name: Chapter 4 Review Round answers to the

College Prep Stats
Chapter 4 Review
Name: _____________________________________
Round answers to the thousandths place, unless otherwise specified.
For numbers 1 – 10, use the data in the accompanying table (based on data from “Helmet Use and Risk of Head Injuries in Alpine
Skiers and Snowboarders,” by Sullheim, eta l., Journal of the American Medical Association, Vol. 295, No. 8).
Head Injuries
Not Injured
Totals
96
656
Wore Helmet
752
480
2330
No Helmet
2810
Totals
576
2986
3562
1. If one of the subjects is randomly selected, find the probability of selecting someone who was not injured.
2. If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet.
3. If one of the subjects is randomly selected, find the probability of selecting someone who had a head injury or did not wear a
helmet.
4. If one of the subjects is randomly selected, find the probability of selecting someone who wore a helmet or was not injured.
5. If one of the subjects is randomly selected, find the probability of selecting someone who wore a helmet and was injured.
6. If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet and was not
injured.
7. If two different study subjects are randomly selected, find the probability that they both wore helmets. (assume without
replacement)
8. If two different study subjects are randomly selected, find the probability that they both had head injuries. (assume without
replacement)
9. If one of the subjects in randomly selected, find the probability of selecting someone who did not wear a helmet, given that the
subject had head injuries.
10. If one of the subjects is randomly selected, find the probability of selecting someone who was not injured, given that the subject
wore a helmet.
11. About 35% of the population has blue eyes (based on a study by Dr. P. Sorita Soni at Indiana University).
a) If someone is randomly selected, what is the probability that he or she does not have blue eyes?
b) If four different people are randomly selected, what is the probability that they all have blue eyes?
c) Would it be unusual to randomly select four people and find that they all have blue eyes? Why or why not?
12. a) If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in
Japan. Ignore leap years.
b) If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years.
13. For a recent year, the fatality rate from motor vehicle crashes was reported as 15.2 per 100,000 population.
a) What is the probability that a randomly selected person will die this year as a result of a motor vehicle crash? Round to 6 decimal
places.
b) If two people are randomly selected, find the probability that they both die this year as the results of motor vehicle crashes. Round
to 9 decimal places.
c) If two people are randomly selected, find the probability that neither of them dies this year as the result of motor vehicle crashes.
Round to 4 decimal places.
14. A spinner has 15 equal sectors, numbered 1 – 15. What is the probability of spinning a number less than 9 or a multiple of 3?
15. A sample of 4 different calculators is randomly selected from a group containing 16 that are defective and 30 that have no defects.
What is the probability that at least one of the calculators is defective?
16. A pollster for the Gosset Survey Company claims that 30 voters were randomly selected from a population of 2,800,000 eligible
voters in New York City (85% of whom are Democrats), and all 30 were Democrats. The pollster claims that this could easily happen
by chance. Find the probability of getting 30 Democrats when 30 voters are randomly selected from this population. Based on the
results, does it seem that the pollster is lying?
17. Based on data from the U.S. Center for Health Statistics, the death rate for males in the 15 – 24 age bracket is 114.4 per 100,000
population, and the death rate for females in that same age bracket is 44.0 per 100,000 population.
a) If a male in that age bracket is randomly selected, what is the probability that he will survive? (express the answer with six decimal
places.)
b) If two males in that age bracket are randomly selected, what is the probability that they both survive? (express the answer with six
decimal places.)
c) If two females in that age bracket are randomly selected, what is the probability that they both survive? (express the answer with
seven decimal places.)
18. Each of two parents has the genotype dimples/no dimples which consist of a pair of alleles that determine your face, and each
parent contributes one of those alleles to a child. Assume that if the child has at least one no dimples allele, that will dominate and
they will not have dimples.
a) List the different possible outcomes.
b) What is the probability that a child will have dimples?
19. If a horse has a probability of winning of 5/9, what are the odds against the horse winning?
20. Assuming the payoff odds are the actual odds you found in #21, if you place a $10 bet to win on that horse, what is the winning
ticket worth?
21. Assume that an actress has a 97% chance of performing in a Broadway show if she gets the part.
a) What is the probability that an actress will not perform in a Broadway show if she gets the part.
b) If you have two actresses, what is the probability they both literally “break a leg” and can’t go on?
c) What is the probability at least one of the actresses will perform? (make sure you use your answer from part b) above)
22. Suppose you are playing a game of chance and your probability of winning is 2:9. What are the odds against winning?
23. Suppose your payoff odds against winning are the actual odds from number 22 above. How much will an $8 bet be worth?
24. A firm uses trend projection and seasonal factors to simulate sales for a given time period. It assigns “0” if sales fall, “1” if sales
are steady, “2” if sales raise moderately, and “3” if sales rise a lot. The simulator generates the following output.
0 1 1 2 0 0 1 1 0 0 2 1 0 1 0 2 1 2 0 1 2 0 2 0 3 1 0 2 1 0 1
Estimate the probability that sales will remain steady.
25. A bag contains 12 orange marbles, 19 yellow marbles, and 15 black marbles. Find
a) P(blue).
b) P(not orange).
c) P(yellow or orange).
26. You are dealt two cards from a shuffled deck of 52 playing cards.
a) Find the probability that both cards are red. The cards are dealt without replacement.
b) Find the probability that both cards are red. The cards are dealt with replacement.
27. A study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after
graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating.
28. Find the odds against correctly guessing the answer to a multiple choice question with 6 possible answers.
29. Two grey mice mate. The male has both a white and grey fur-color gene. The female has only grey fur-color genes. The fur color
of the offspring depends on the fur-color genes that they receive. Assume that neither the white nor the grey gene dominates. List the
unique possible outcomes.
30. Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are made and each
question has 6 possible answers. (express answer to four decimal places.)
31. An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at least
one correct answer.
32. A tourist in France wants to visit 12 different cities. How many different routes are possible?
33. Eight basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the
players are selected randomly, what is the probability that the 8 tallest players will be selected?
34. How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
35. A tourist in France wants to visit 7 different cities. If the route is randomly selected, what is the probability that she will visit the
cities in alphabetical order? (express answer to four decimal places.)
36. A state lottery involves the random selection of six different numbers between 1 and 25. If you select one six number
combination, what is the probability that it will be the winning combination?
37. Describe the simulation using one 6 sided die: The probability of having a boy when a child is born.
38. Simulate the probability that 4 members of a family were each born on a different day of the week. Run randInt(1,7, 4).
a) What does each number, one through seven, represent?
b) What does the four represent?
c) Complete 10 trials to determine the probability that 4 members of a family were each born on a different day of the week.
The remaining problems are EXTRA PRACTICE
39. Of the 84 people who answered “yes” to a question, 14 were male. Of the 73 people that answered “no” to the same questions, 12
were male. Fill in the table below and use the table to answer the probability questions.
Responded “yes”
Responded “no”
Total
Male
14
12
26
Female
70
61
131
Total
84
73
157
a) If one person is selected at random from the group, what is the probability that the person was a female?
b) If one person is selected at random from the group, what is the probability that the person answered “yes” or was male?
c) If one person is selected at random from the group, what is the probability that the person answered “yes” and was male?
d) If one person is selected at random from the group, what is the probability that the person answered “no” or was female?
e) If two people are selected at random from the group, what is the probability that the first person answered yes and the second
person answered no? (assume without replacement)
f) If two people are selected at random from the group, what is the probability that both of them were males? (assume without
replacement)
40. An allergist conducts a study to determine allergies to cats.
Allergic
Positive
139
Negative
27
Total
166
Not Allergic
16
297
313
Total
155
324
479
a) If one of the test subjects is randomly selected, find the probability that the subject tested positive or was allergic to cats.
b) If one of the test subjects is randomly selected, find the probability that the subject was not allergic to cats.
c) Find the probability of a false negative or a false positive.
41. All of the letters of the alphabet are written on identical slips of paper and placed into a hat and mixed up really well. Find
a) P(selecting one slip of paper and it having a vowel written on it). Do not include Y as a vowel.
b) P(selecting one slip of paper and it having a consonant written on it).
c) P(L or Q).
42. If you are told that a mystery person's name begins with a consonant, would it be "unusual" to guess the first letter of that person's
name?
.
43. In a certain class of students, there are 10 boys from Wilmette, 6 girls from Kenilworth, 6 girls from Wilmette, 5 boys from
Glencoe, 3 boys from Kenilworth and 5 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the
probability that the student will be from Kenilworth?
44. In one town, 39% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are
both Democrats.
45. In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without replacement from the
8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire
batch will be rejected?
46. A medical testing laboratory saves money by combining blood samples for tests. The combined sample tests positive if at least one
person is infected. If the combined sample tests positive, then the individual blood tests are performed. In a test for Chlamydia, blood
samples from 10 randomly selected people are combined. Find the probability that the combined sample tests positive with at least one
of the 10 people infected. Based on data from Centers for Disease Control, the probability of a randomly selected person having
Chlamydia is 0.00320. Is it likely that such combined samples test positive?