Probability And Statistics Worksheets Page 6
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42The set of all possible outcomes of an experiment is called the
Problem Solving
sample space.
Tip
Probability is often
E x a m p l e 2
expressed as a percent.
A percent is a ratio of a
number compared to 100.
SPORTS
A baseball team has 8 pitchers and 3 catchers. The
For example, 87% means
manager is choosing a pitcher-catcher combination. How many
8
7
are possible?
87 : 100 or
or 0.87.
1
0
0
A decimal can be
converted to a percent
Solution
by moving the decimal
two places to the right.
One way to show all possible outcomes is to use ordered pairs. For
So, 0.4 can also be written
example, use the numbers 1–8 for pitchers and the letters A–C for
as 40%.
the catchers.
(1, A)
(2, A)
(3, A)
(4, A)
(5, A)
(6, A)
(7, A)
(8, A)
(1, B)
(2, B)
(3, B)
(4, B)
(5, B)
(6, B)
(7, B)
(8, B)
(1, C)
(2, C)
(3, C)
(4, C)
(5, C)
(6, C)
(7, C)
(8, C)
There are 24 possible pitcher-catcher combinations.
Another way to show the sample space is to use a
Pitchers
Catchers
Outcomes
tree diagram.
A
(1, A)
1
B
(1, B)
You can use probability to predict the number of
C
(1, C)
times an event will occur.
A
(2, A)
2
B
(2, B)
C
(2, C)
E x a m p l e 3
A
(3, A)
3
B
(3, B)
C
(3, C)
SPORTS
A softball player has had 24 hits in her
A
(4, A)
first 60 times at bat. Predict her total number of
4
B
(4, B)
hits in 330 at bats.
C
(4, C)
A
(5, A)
Solution
5
B
(5, B)
C
(5, C)
First, use the outcomes that have already occurred
A
(6, A)
to find the experimental probability of the player
6
B
(6, B)
getting a hit each time at bat.
C
(6, C)
A
(7, A)
2
4
P(hit)
0.4
7
B
(7, B)
6
0
C
(7, C)
Then multiply that result by the total number of
A
(8, A)
times at bat.
8
B
(8, B)
C
(8, C)
0.4(330)
132
Based on the player’s first 60 times at bat, you can predict that she will get
132 hits in 330 at bats.
As you increase the number of trials in a probability experiment, the
experimental probability will probably get closer to the theoretical probability. For
1
example, when tossing a fair coin, P(heads)
. The more often you toss the
2
coin, the closer you will come to tossing an equal number of heads and tails.
385
Lesson 9-1 Review Percents and Probability
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