Download What is the range of possible outcomes? The Range of Probability

Lesson
5 Problem Solving:
The Range of Probability
Monitoring Progress:
Quiz 1
Problem Solving: The Range of Probability
What is the range of possible outcomes?
Let’s think about the chances of winning a raffle. There are 100
tickets in a box, and there is going to be one winner. We purchased 5
tickets. The total number is 100.
Our chance of winning is 5 out of 100, or 5%:
5
100
= 0.05 = 5%
Now let’s think about the total range of what is possible. Let’s say
we didn’t think the chances of winning the raffle were very good. We
decided not to buy a ticket. What are our chances now? If we don’t have
a ticket, there is no way to win.
The probability of winning is 0.00 or 0%:
0
100 = 0.00 = 0%
Now let’s look at the other extreme. We want to win so badly that we
were first in line to buy tickets. We bought all 100 tickets. Now we know
that one of our numbers will have to be picked from the box. We are
certain of it.
Our chances of winning are 1.00 or 100%:
100
100 = 1.00 = 100%
502 Unit 7 • Lesson 5
Vocabulary
complementary
events
Lesson 5
These extremes are important because they show the entire range
of probability. They go from no chance of winning to complete
certainty. The range is from 0 to 1.
0
No Chance
1.00
Certain
The probability of an
event occurring is always
a number between 0
and 1.
When we describe probability, we use decimal numbers that range
from 0.00 to 1.00. There is no way that we could have anything less
than a 0.00 chance. There is no way that we could have more than
1.00 chance.
Improve Your Skills
Your friend found the probability of having a single coin land heads up.
She says the probability is 2, since there are two sides of the coin.
Since a probability has to be between 0 and 1, we know that your
friend’s answer is incorrect.
ERROR
The probability of having a coin land heads up is 1
2 . We know this is a
CORRECT
reasonable probability because 1
2 is between 0 and 1.
Unit 7 • Lesson 5 503
Lesson 5
What is the chance that something
won’t happen?
We learned how to figure the probability of something happening. But
what about the probability that something will not happen? Let’s find
out how to calculate the chance of an event not happening.
Sometimes even a great basketball player has a hard time making free
throws. Let’s say, on average, the player makes 7 out of 10 free throws.
What are the chances this player will make his next free throw?
The chances are 7 out of 10. We can describe the probabilities this way.
7
10 = 0.70 or 70%
What are the chances the player will not make the next free throw? To
figure it out, we subtract the probability from 1.00. Remember that
a probability of 1.00 means something will happen every time. The
decimal number 1.00 is the same as 100 percent. Example 1 shows how
to find the chances, or probability, of something not happening.
Example 1
Show the probability that a basketball player will not make a
free throw.
We always start with 1.00. Then we subtract the probability that an
event will happen. The probability the player will make the next free
throw is 0.70. So we subtract 0.70 from 1.00.
1.00 − 0.70 = 0.30 or 30%
We end up with the probability that it will not happen.
The chances of not making the next free throw are 0.30 or 30 percent.
The probability the basketball player will make the next free
throw, and the probability he will miss the next free throw are
called complementary events . They complement each other to
make a total of 100 percent. We see that 70% + 30% = 100%.
Problem-Solving Activity
Turn to Interactive Text,
page 261.
504 Unit 7 • Lesson 5
Monitoring Progress
Quiz 1
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 5
Homework
Activity 1
Write each of the numbers using scientific notation.
1. 340 2. 2,200 3. 42,000 4. 370,000 5. 8,000 6. 1,300,000 Activity 2
Tell the probability of each of the complementary events.
ModelIf there’s a 60% chance of rain, what is the chance it will not rain?
Answer: 40% (60% + 40% = 100%)
1. If the basketball player has a 45% chance of making a free throw, what is
the chance he will not make it? 2. If the chance of drawing a king from a deck of cards is about 8%, what are
the odds of not selecting a king? 3. If there is a 25% chance that you will win a carnival game, what is the
chance you will not win? 4. What are the odds a coin will not land on tails when you toss it? 5. What are the odds you will not draw a card that’s a club from a regular deck
of cards? 6. What are the odds you will not roll a 6 on a die? 5
6
Activity 3 • Distributed Practice
Solve.
5
1. Write 10 as a percent. 2. Write 0.005 as a fraction. 3. Write 1% as a decimal number.
4.
5. 5 · 0.134 6. 64.8 + 92.8 + 57.19 2
1
7. 27 9 + 19 3 5
9
8.
1
2
3
7
+ 28 · 48 3
4
5
1,000
3
14
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Unit 7 • Lesson 5 505