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Lesson 6.2.1Lesson 6.2.1

ProbabilityProbability

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Lesson

6.2.1ProbabilityProbability

California Standard:Statistics, Data Analysis, and Probability 3.3Represent 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

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ProbabilityProbability

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.

Lesson

6.2.1

Probability is a way of using numbers to describe the chance of an event happening.

What are the chances that I will roll a six?

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ProbabilityProbability

Some Events Are More Likely to Happen Than Others

Lesson

6.2.1

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?”

Impossible Very unlikely

Fairly unlikely

Even chance

Quite likely

Very likely

Certain

Look at the line below and think about where your answer would be for each of these questions.

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Impossible Very unlikely

Fairly unlikely

Even chance

Quite likely

Very likely

Certain

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Guided Practice

Solution follows…

Lesson

6.2.1

Decide where you would put the chances of the following events happening on this scale:

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

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Impossible Very unlikely

Fairly unlikely

Even chance

Quite likely

Very likely

Certain

ProbabilityProbability

Guided Practice

Solution follows…

Lesson

6.2.1

Decide where you would put the chances of the following events happening on this scale:

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

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Guided Practice

Solution follows…

Lesson

6.2.1

7. Put the events named in Exercises 1–6 in order, from most likely to least likely.

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.

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.

Most likely Least likely1 254 36

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ProbabilityProbability

Probability Is a Way to Say How Likely an Event Is

Lesson

6.2.1

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% or 50%

1

2

1 or 100%

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ProbabilityProbabilityLesson

6.2.1

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.

0% 50% 100%

1

20 1

A probability of (or 50%) means that the event

might happen, but there’s an equal chance that it won’t.

1

2

10

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.

ProbabilityProbability

Guided Practice

Solution follows…

Lesson

6.2.1

Estimate the probability that each of the following things will happen. Write your answers as percents.

100%

0%

About 50%

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11. Which of the probabilities above represents an impossible event?

12. Which of the probabilities above represents a certain event?

ProbabilityProbability

Guided Practice

Solution follows…

Lesson

6.2.1

Use the list of probabilities below to answer Exercises 11–12.

12

1010

025

58

025

1010

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Probability Is Usually Calculated Exactly

Lesson

6.2.1

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.

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Spinning the color red is certain, so the probability is 1.

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Example 1

What is the probability of spinning the color red on this spinner?

What is the probability of spinning the color blue?

Solution follows…

Lesson

6.2.1

Solution

Spinning the color blue is impossible, so the probability is 0.

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The blue section is one-fourth of the spinner.

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Example 2

What is the probability of spinning the color blue on this spinner?

Solution follows…

Lesson

6.2.1

Solution

So the probability of spinning the color blue is

If you spun the spinner lots of times, about one-fourth of the spins would land on blue.

= 0.25 = 25%1

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Guided Practice

Solution follows…

Lesson

6.2.1

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 It is impossible to spin pink, so the probability is 0.

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.

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ProbabilityProbability

Guided Practice

Solution follows…

Lesson

6.2.1

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.

14

13

15

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Independent Practice

Solution follows…

Lesson

6.2.1

Each set of cards shown below is turned over and shuffled, then one card is picked.

A. B.

C. D.

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:

0 114

15

15

14

250

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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?

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Independent Practice

Solution follows…

Lesson

6.2.1

A bag has 1 red, 1 blue, and 2 yellow marbles in it.

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1

1

2

14

14

12

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Independent Practice

Solution follows…

Lesson

6.2.1

7. The probability of an event occurring is .

Which two values below represent this same probability?

55 5.5

8. The probability of an event occurring is 55%. Which two values below represent this same probability?

38

0.375 375% 0.375% 37.5%38

%

0.55100

55100

1120

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Independent Practice

Solution follows…

Lesson

6.2.1

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

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Round UpRound 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.

Lesson

6.2.1