For more practice, see Extra Practice.
EXERCISES
A Practice by Example
Example 1
(page 612)
Example 2
(page 612)
Find each probability. One letter of the alphabet appears on each of 26
cards. You choose a card at random and then replace it. Then you choose a
second card. Assume Y is a consonant.
1. P(I and a vowel)
2. P(Z and a consonant)
3. P(a vowel and a consonant)
4. P(2 vowels)
5. P(A and B)
6. P(C and X)
Find each probability. A bag contains the following marbles: 6 red,
4 orange, 3 yellow, 2 blue, and 5 green. You choose a marble at random and
do not replace it. Then you select another marble.
7. P(red and blue)
B Apply Your Skills
8. P(red and yellow)
9. P(orange and blue)
10. P(blue and green)
11. P(blue and yellow)
12. P(orange and red)
Find each probability. Suppose you roll a
number cube and spin the spinner at the right.
Express your answer as a percent rounded to the
nearest tenth.
13. P(3 and green)
14. P(prime and blue)
15. P(5 and yellow)
16. P(8 and yellow)
B
Y
B
G
G
G
Y
G B
Y
17. P(an even number and green)
18. a. School Carnival For a carnival game, a number cube is rolled. Each
of its six faces has a different color. To win, you must select the color
rolled. Find the probability of playing the carnival game twice and
winning both times.
b. Disjoint events are events with no outcomes in common. To nd the
probability of two disjoint events, add the probabilities of the
individual events. Suppose for the game, you choose red and your
friend picks blue. What is the probability that either you or your
friend wins?
19. a. Data File, p. 589 You plan to visit two different zoos but cannot decide
which two to visit. On a piece of paper, you write the name of each zoo
in the table. Then you select the names of two zoos at random. Are
your selections independent or dependent events? Explain.
b. What is P(Smithsonian and El Paso)?
20. Writing in Math What is the difference between independent and
dependent events? Explain.
11-5 Independent and Dependent Events
613–616
State whether the events are dependent or independent. Explain.
21. Toss a coin. Then roll a number cube.
22. Select a card. Replace it. Then select another card.
23. Select a card. Do not replace it. Then select another card.
24. Spin a spinner once. Then spin the spinner again.
25. Select a marble from a bag. Put it aside. Then select another marble.
C
Challenge
26. Mazes Find the probability of a mouse locating the cheese on its first
attempt in the maze. Assume the mouse selects each path at random.
27. Algebra If two events are dependent and P(event) = ba , then what is
P(event and event)?
28. Stretch Your Thinking Two ants race around the perimeter of a unit
square. They both start at the same vertex and move clockwise. One ant
runs at the constant rate of 1 unit per second. The other ant runs at the
constant rate of 2 units per second. How far apart will they be after
17 seconds?
613–616
Chapter 11 Probability
Test Prep
Reading Comprehension
Read the passage and answer the questions below.
Colorblindness
Most people who are colorblind
do not see the world in black and
white. In fact, there are many
different types of colorblindness.
A person who sees only black and
white is extremely rare.
Colorblindness occurs when the
cones in the retina of the eye are
sensitive to the wrong wavelength
of light. One study indicates that
5% of men and 0.5% of women
are colorblind.
29. Find the probability that two men chosen at random are colorblind.
30. Find the probability that two women chosen at random are colorblind.
Multiple Choice
31. A pack of juice boxes contains 4 apple, 4 cherry, 4 orange, and
4 grape boxes. If you and a friend each select a juice box at random,
what is the probability that you will both get grape?
3
A. 64
Take It to the NET
Online lesson quiz at
www.PHSchool.com
Web Code: aca-1105
1
B. 20
1
C. 4
1
D. 2
32. Of a set of 10 cards, 3 have red circles, 4 have yellow triangles, and
3 have green diamonds. You choose one card at random and then
replace it. Then you choose a second card. What is the probability
that both cards have yellow triangles?
3
F. 25
2
G. 15
4
H. 25
I. 2
5
Mixed Review
Lesson 11-4
Lesson 9-8
A spinner is divided into 7 equal sections that are numbered from 1 to 7.
You spin the spinner once. Find each probability.
33. P(5)
34. P(3 or 7)
35. P(even number)
36. P(not 8)
37. P(not 5)
38. P(odd number)
39. Gardening A gardener has 190 ft of fencing and wants to enclose the
greatest possible area for a garden. What dimensions should he use?
Draw a diagram and then make a table to find the solution.
11-5 Independent and Dependent Events
613–616
Practice Game
Analyzing Fair Games
What You’ll Need
sets of four chips with red on one side and yellow on the other side of
each chip, as shown at the right
How To Play
• Decide who is Player A and who is Player B.
• Each player tosses the chips once. If all four chips are the same color,
Player A scores a point. If not, Player B scores a point.
• The first player to reach 20 points is the winner.
1. Make an organized list of all possible outcomes. Which is more likely,
exactly 1, exactly 2, exactly 3, or exactly 4 red sides up?
2. Reasoning Is this game fair? Explain.
3. Suppose you toss the chips twice. What is the probability that you get
exactly 1 red side up twice?
613–616
Chapter 11 Probability