1. Probability
Lesson 6.2.1

2. Probability 6.2.1 California Standard: What it means for you:
Lesson
6.2.1
Probability
California Standard:
Statistics, Data Analysis, and Probability 3.3
Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1–P is the probability of an event not occurring.
What it means for you:
You’ll learn about using probability as a way to describe how likely events are to happen.
Key words:
probability
chance
likely
percent
fraction
decimal

3. What are the chances that I will roll a six?
Lesson
6.2.1
Probability
A lot of the time, you can’t say for sure whether or not one particular event will happen. But you can often say how good the chances are.
What are the chances that I will roll a six?
Probability is a way of using numbers to describe the chance of an event happening.

4. Probability 6.2.1 Some Events Are More Likely to Happen Than Others
Lesson
6.2.1
Probability
Some Events Are More Likely to Happen Than Others
People often talk about things that might happen, using words like “chance,” “likely,” and “probability”:
“What is the probability it will snow today?”
“How likely is it that the school football team will win its next game?”
“What is the chance that you will go to a movie this weekend?”
Look at the line below and think about where your answer would be for each of these questions.
Impossible
Very unlikely
Fairly unlikely
Even chance
Quite likely
Very likely
Certain

5. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
Decide where you would put the chances of the following events happening on this scale:
Impossible
Very unlikely
Fairly unlikely
Even chance
Quite likely
Very likely
Certain
1. Leaves falling from the trees next fall.
2. Finding a live elephant in your bedroom when you get home.
3. Winning a raffle if you have 1 out of 100 tickets.
Certain
Very very unlikely
Very unlikely
Solution follows…

6. 6.2.1 Probability Probability Guided Practice
Lesson
6.2.1
Probability
Probability
Guided Practice
Decide where you would put the chances of the following events happening on this scale:
Impossible
Very unlikely
Fairly unlikely
Even chance
Quite likely
Very likely
Certain
4. Winning a raffle if you have 99 out of 100 tickets.
5. Winning a raffle if you have 1 out of 1,000,000 tickets.
6. A tossed coin landing on heads.
Very likely
Very very unlikely
Even chance
Solution follows…

7. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
7. Put the events named in Exercises 1–6 in order, from most likely to least likely.
Leaves falling from the trees next fall.
Finding a live elephant in your bedroom when you get home.
Winning a raffle if you have 1 out of 100 tickets.
Winning a raffle if you have 99 out of 100 tickets.
Winning a raffle if you have 1 out of 1,000,000 tickets.
A tossed coin landing on heads.
Most likely 1 4 6 3 5 2
Least likely
Solution follows…

8. Probability 6.2.1 Probability Is a Way to Say How Likely an Event Is
Lesson
6.2.1
Probability
Probability Is a Way to Say How Likely an Event Is
In math, probability is a way of describing the chance that an event will occur. Probability can be written using fractions, decimals, or percents.
You can replace the words on the line below with numbers that represent how likely an event is to occur:
Impossible
Very unlikely
Fairly unlikely
Even chance
Quite likely
Very likely
Certain
0 or 0%
1 or 100%
or 50% 1 2

9. Lesson
6.2.1
Probability 0%
50%
100% 1 2
A probability of 0 (or 0%) means that there is no chance.
A probability of 1 (or 100%) means that the event will definitely happen.
A probability of (or 50%) means that the event
might happen, but there’s an equal chance that it won’t. 1 2

10. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
Estimate the probability that each of the following things will happen. Write your answers as percents.
8. It will go dark tonight.
9. Your math teacher will turn into a pineapple.
10. A 6th-grader from California chosen at random will be a girl.
100% 0%
About 50%
Solution follows…

11. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
Use the list of probabilities below to answer Exercises 11–12. 1 2 5 8 25 10
11. Which of the probabilities above represents an impossible event?
12. Which of the probabilities above represents a certain event? 25 10
Solution follows…

12. Probability 6.2.1 Probability Is Usually Calculated Exactly
Lesson
6.2.1
Probability
Probability Is Usually Calculated Exactly
There are many situations where you can say exactly what the probability of an event is.
This isn’t the same as saying whether an event will definitely (or not definitely) happen — it’s just a measure of how likely the event is.

13. Lesson
6.2.1
Probability
Example 1
What is the probability of spinning the color red on this spinner?
What is the probability of spinning the color blue?
Solution
Spinning the color red is certain, so the probability is 1.
Spinning the color blue is impossible, so the probability is 0.
Solution follows…

14. Lesson
6.2.1
Probability
Example 2
What is the probability of spinning the color blue on this spinner?
Solution
The blue section is one-fourth of the spinner.
So the probability of spinning the color blue is
= 0.25 = 25% 1 4
If you spun the spinner lots of times, about one-fourth of the spins would land on blue.
Solution follows…

15. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
Exercises 13–15 are about this spinner.
Find the probability of spinning the colors below.
Write your answers as decimals.
13. Blue
14. Yellow
15. Pink
Half the spinner is blue, so the probability of spinning blue is one-half or 0.5.
Half the spinner is yellow, so the probability of spinning yellow is one-half or 0.5.
It is impossible to spin pink, so the probability is 0.
Solution follows…

16. Probability 6.2.1 Guided Practice
Lesson
6.2.1
Probability
Guided Practice
In Exercises 16–18, find the probability of spinning the color yellow on each of the following spinners.
Write your answers as fractions.
16.
17.
18. 1 4 1 3 1 5
Solution follows…

17. Probability 6.2.1 Independent Practice
Lesson
6.2.1
Probability
Independent Practice
Each set of cards shown below is turned over and shuffled, then one card is picked. A. B. C. D. A: B: C: D:
1. a triangle card
2. a star card
For each set of cards, find the probability of picking: 1 4 1 5 1 5 1 4 2 5 1
Solution follows…

18. Probability 6.2.1 Independent Practice
Lesson
6.2.1
Probability
Independent Practice
A bag has 1 red, 1 blue, and 2 yellow marbles in it.
3. How many marbles are in the bag?
4. How many marbles are red? What is the probability of drawing a red marble?
5. How many marbles are blue? What is the probability of drawing a blue marble?
6. How many marbles are yellow? What is the probability of drawing a yellow marble? 4 1 1 4 1 1 4 2 1 2
Solution follows…

19. Probability 6.2.1 Independent Practice
Lesson
6.2.1
Probability
Independent Practice
7. The probability of an event occurring is Which two values below represent this same probability? 3 8
0.375
375%
0.375%
37.5% 3 8 %
8. The probability of an event occurring is 55%. Which two values below represent this same probability?
0.55
100 55
100 11 20 55
5.5
Solution follows…

20. Probability 6.2.1 Independent Practice
Lesson
6.2.1
Probability
Independent Practice
9. In a tiled hallway, kids are jumping from one tile to the next. The probability of landing on a green tile is 60%.
What fraction of the hallway area is covered with green tiles? 3 5
Solution follows…

21. Lesson
6.2.1
Probability
Round Up
Probability is useful because you can use it to compare the chances of different events happening.
The event with the highest probability is the most likely to occur.