Probability and Statistics – Mrs. Leahy
Unit 4 Homework Problems (Elementary Probability Theory)
Section 1
1. List three methods of assigning probabilities.
2. Suppose the newspaper states that the probability of rain today is 30%.
a) What is the complement of “rain today”? b) What is the probability of the complement?
3. What is the probability of
a) an event A that is certain to occur?
b) an event B that is impossible?
4. Textbook pg 338 #6
5. Textbook pg 338 #7
6. Textbook pg 338 #10
7. Textbook pg 338 #11
8. Textbook pg 338 #12
9. a) What is the law of large numbers?
b) If you were using the relative frequency of an event to estimate the probability of the event, would it be
better to use 100 trials or 500 trials? Explain.
10. Textbook pg 341 #44
11.
a) Explain why -0.41 cannot be the probability of some event.
b) Explain why 1.21 cannot be the probability of some event.
c) Explain why 120% cannot be the probability of some event.
d) Can the number 0.56 be the probability of an event? Explain.
12. John runs a computer software store. Yesterday he counted 127 people who walked by his store, 58 of whom
came into the store. Of the 58, only 25 bought something in the store.
a) Estimate the probability that a person who walks by the store will enter the store.
b) Estimate the probability that a person who walks into the store will buy something.
c) Estimate the probability that a person who walks by the store will come in and buy something.
d) Estimate the probability that a person who comes into the store will buy nothing.
13. Textbook p339 #25
14. Textbook p340 #26
15. Textbook p340 #31a
16. Textbook pg 340 #32a
Section 2
17. pg 361 #5
18. pg 362 #10
19. For an arch chosen at random in
Arches National Park, use the information
in the table to estimate the given
probabilities about the heights of arch
openings.
a) P(3 to 9 feet)
b) 30 feet or taller
c) less than 75 feet
Questions 20-25 refer to the following:
Diagnostic tests of medical conditions have several types of
results. The test result can be positive or negative even if a
patient does not have the condition. A positive test (+)
indicates that the patient has the condition. A negative test
( - ) indicates that the patient does not have the condition.
Remember that a positive test does not prove the patient
has the condition. Consider a random sample of 200
patients. Results of a new diagnostic test for the condition are shown.
20.
21.
22.
23.
24.
25.
P( +|condition present)
P( - |condition present)
P( - |condition absent)
P( +|condition absent)
P( + and condition present)
P ( - and condition absent)
Questions 26 –
30 refer to the
following:
Use the table to
find each
probability. The
tables gives
information
about students
at one school.
26.
27.
28.
29.
30.
P(sports)
P(female)
P(hiking | male)
P(male | hiking)
P(reading and female)
this is known as the sensitivity of the test
this is known as the false negative rate.
this is known as the specificity of the test
this is known as the false positive rate
Section 3
31. pg 341 #35
32. pg 341 #36
33. pg 341 #38
34. pg 362 #17
Questions 35 -37 refer to the following:
You roll two fair dice, one green and one red.
35. Are the outcomes on the dice independent?
36. Find P(1 on the green die and 2 on the red die)
37. Find P(even on the green die and less than 5 on the red die)
Questions 38-41 refer to the following
You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first on
back and reshuffle the deck.
38. Are the outcomes on the two cards independent?
39. Find the P(3 on 1st card and red on 2nd card)
40. Find P(10 on 1st card and 3 on second card)
41. Find P(Red on first card and red on second card)
Section 4
42. pg 341 #42
43. pg362 #13
44..
45. You need to know the number of different arrangements for five distinct letters. You decide to use the
permutations rule, but your friend tells you to use 5!. Who is correct? Explain.
46. Draw a tree diagram to display all the possible head-tail sequences that can occur when you flip a coin three
times.
47. What is the probability that you will get exactly two heads when you toss a coin three times? (Use your tree
diagram from the previous question to help you answer this!)
48. Draw a tree diagram to display all the possible outcomes when you flip a coin then toss a die.
49. What is the probability that you will get a head AND a number greater than 4 when you flip a coin and toss a
die? (Use your tree diagram from the previous question to help you answer this!)
50. There are six marbles in a jar. They are identical except for color. Two are red, three are blue, and one is
yellow. You are to draw a marble from the jar, note its color, and set it aside. Then you are to draw another
marble. Make a tree diagram to show all possible outcomes of the experiment.
51. Calculate the probabilities of each possible outcome in the experiment above. For example P(red, red), P(red,
blue), etc.
52. A sales representative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. In how many ways
(orders) can the representative visit the four cities?
53. A research biologist is studying the effects of fertilizer type, temperature, and water treatment. She has four
different fertilizer types, three temperature zones, and three water treatments to test. Determine the number of
different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment
configuration.
54. A professor grades homework by randomly choosing 5 of 12 homework problems to grade. How many
different groups of 5 problems can be chosen from the 12 problems?
55. A qualified applicant pool for six equal management trainee positions contains 12 people. How many ways
can the positions be filled?
56. There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor;
position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 15
candidates qualified for all three positions. Determine the number of different ways the positions can be filled by
these applicants.
57. How many ways can 1st, 2nd, and 3rd place be awarded to 20 different contestants in a competitive eating
event?