Topic 11 - Statistics and Probability
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a
marble at random without looking. Find the probability of each event. Write your answer as a fraction in
simplest form.
____
____
1. P(red)
a.
c.
b.
d.
2. P(blue)
a.
c.
b.
____
d.
3. P(red or white)
a.
c.
b.
____
d.
4. P(blue or purple)
a.
c.
b.
____
d.
5. P(not white)
a.
c.
b.
d.
During lunch at Urbana Middle School today, several students have brought their lunch from home and
several students are ordering a school lunch as shown in the table. Suppose one student is randomly selected
during lunch time. Find the probability of each event. Write as a fraction in simplest form.
Brought lunch from home
Order school lunch
6th Graders
7th Graders
8th Graders
____
6. P(order school lunch)
a.
b.
____
7. P(6th grader)
55
45
32
35
33
c.
d.
____
a.
c.
b.
d.
8. P(not 7th grader)
a.
b.
____
c.
d.
9. P(brought lunch from home or ordered school lunch)
a.
c.
b.
____ 10. P(7th grader or 8th grader)
a.
b.
d. 1
c.
d.
For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
____ 11. tossing a nickel and tossing a quarter
a. 2
c. 6
b. 4
d. 8
____ 12. picking a number from 1 to 4 and choosing the color red, green, or yellow
a. 6
c. 12
b. 9
d. 24
____ 13. choosing a blue, white, or green shirt with khaki or denim pants
a. 6
c. 12
b. 3
d. 10
____ 14. choosing either turkey or ham on wheat or rye bread
a. 2
c. 4
b. 8
d. 12
____ 15. rolling a number cube and choosing a card between the cards marked X and Y
a. 6
c. 8
b. 20
d. 12
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
____ 16. rolling a number cube and tossing a nickel
a. 6
c. 24
b. 8
d. 12
____ 17. choosing a number from 1 to 15 and a vowel from the word COUNTING
a. 120
c. 90
b. 45
d. 55
____ 18. choosing a car with an exterior color of black, red, green, gray, or tan; and choosing a leather or fabric interior
a. 10
c. 15
b. 20
d. 8
____ 19. choosing a tuna, turkey, or cheese sandwich; on wheat or white bread; with a side of potato chips, corn chips,
or baked potato
a. 18
c. 8
b. 24
d. 9
____ 20. choosing a card from a deck of cards numbered 10, 11, 12, ..., 25 and picking a day of the week
a. 175
c. 112
b. 124
d. 156
Glenn surveyed 40 of his classmates to determine their favorite cafeteria food. The results of his survey are
shown in the table.
Favorite
Food
Meatloaf
Tacos
Hamburgers
Pizza
Fish
Number of
Students
4
5
9
18
4
____ 21. What is the probability of meatloaf being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 22. What is the probability of pizza being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 23. What is the probability of tacos being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 24. Suppose there are 200 students in the cafeteria during lunch. How many students would you expect to choose
hamburgers as their favorite cafeteria food?
a. 50
c. 45
b. 9
d. 36
____ 25. Suppose there are 200 students in the cafeteria during lunch. How many students would you expect to choose
pizza as their favorite cafeteria food?
a. 90
c. 18
b. 104
d. 72
A standard deck of playing cards contains 52 cards. The deck is divided into 4 suits of 13 cards each: hearts,
diamonds, clubs, and spades. Hearts and diamonds are red suits, and clubs and spades are black suits.
Suppose a card is drawn from the deck and recorded. Then the card is reinserted into the deck, the deck is
shuffled, and a second card is drawn and recorded. Find each probability.
____ 26. P(2 spades)
a.
c.
b.
d.
____ 27. P(2 red cards)
a.
c.
b.
d.
____ 28. P(red card on the first draw, club on the second draw)
a.
c.
b.
d.
____ 29. P(Jack on the first draw, heart on the second draw)
a.
c.
b.
d.
____ 30. P(black Ace on the first draw, red King on the second draw)
a.
c.
b.
d.
Short Answer
A deck of 24 cards is numbered 1, 2, 3, ... 24. Suppose you pick a card at random without looking. Find the
probability of each event. Write as a fraction in simplest form.
31. P(21)
32. P(10 or 15)
33. P(odd number)
34. P(greater than or equal to 19)
35. P(factor of 9)
The drama club at Fairborn Middle School is putting on a play for parents, teachers, and students. The club
is made up of the students shown in the table. Suppose one student is randomly selected to read an
announcement for the play over the public address system. Find the probability of each event. Write as a
fraction in simplest form.
Boys
Girls
6th Graders
7th Graders
8th Graders
22
18
10
15
15
36. P(boy)
37. P(girl or boy)
38. P(7th grader or 8th grader)
39. P(not 8th grader)
40. P(6th grader or 8th grader)
For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
41. choosing pepperoni or mushroom pizza on thin crust or regular crust
42. choosing a letter from the word MATH and choosing a letter from the word FUN
43. choosing a silver, black, or red CD player and choosing a rock, country, or rap CD
44. tossing a coin and choosing a consonant from the word ALGEBRA
45. tossing a penny, tossing a dime, and choosing a card between the cards marked A, B, and C
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
46. choosing an outfit from 6 shirts, 4 pants, and 3 jackets
47. choosing a plain, sesame, sourdough, or blueberry bagel, with chives, plain, or vegetable spread
48. picking a day of the week and a date in the month of April
49. choosing a password that consists of one letter and two numbers from 1 to 9
(Note: the digits can be repeated.)
50. choosing a card from a standard deck of 52 playing cards and rolling a number cube
Solve.
51. A green and a white number cube are rolled. What is the probability that a 3 or a 4 is rolled on the green cube
and an even number is rolled on the white cube?
52. A coin is tossed 4 times. What is the probability of heads on the first toss, tails on the second toss, and heads
on the third and fourth tosses?
53. Horatio rolls a red number cube, rolls a blue number cube, and then tosses a quarter. What is the probability
that he rolls an even number on the red cube, an odd number on the blue cube, and the coin lands on heads?
A bag contains 4 green tokens, 2 red tokens, and 4 purple tokens. Lisa drew a token out of the bag, recorded
the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar
graph. Use this information to answer the following questions.
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Green
Red
Purple
54. What is the theoretical probability of drawing a red token?
55. What was the experimental probability of drawing a red token? Discuss any differences between this
probability and the theoretical probability of drawing a red token.
56. What is the theoretical probability of drawing a purple token?
57. What was the experimental probability of drawing a purple token? Discuss any differences between this
probability and the theoretical probability of drawing a purple token.
58. Suppose Lisa repeats the experiment an additional 250 times and records the results. About how many times
would you expect her to draw a green token?
Essay
59. A deli offers sub sandwiches on wheat or rye bread, with a choice of ham, salami, or turkey. The deli also
offers customers a choice of American, Provolone, or Cheddar cheese. Suppose a sandwich is chosen at
random.
a. Make a tree diagram that shows all of the possible outcomes.
b. What is the probability that a randomly selected sandwich will be ham on rye with American
cheese?
c. What is the probability that a randomly selected sandwich will contain Provolone cheese or
salami?
60. Maureen baked different kinds of cookies and put them in a cookie jar. The jar contains 4 peanut butter, 6
chocolate chip, 3 oatmeal, and 7 sugar cookies. Assuming the cookies are randomly distributed in the cookie
jar, find each probability.
a.
Suppose Maureen’s brother selects 3 cookies from the jar. What is the probability that
he will select a chocolate chip cookie, then a sugar cookie, and then another chocolate
chip cookie?
b.
Does the situation described in part a represent a set of independent or dependent
events? Explain.