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Objective

Find experimental probability

Vocabulary

Experimental probability

An estimated probability based on the relative frequency of positive outcomes occurring

during an experiment

Vocabulary

Theoretical probability

Probability based on known characteristics or facts

Vocabulary

Proportion

A statement of equality of two or more ratios

Example 1 Experimental Probability

Example 2 Experimental Probability

Example 3 Theoretical Probability

Example 4 Experimental Probability

Example 5 Use Probability to Predict

Example 6 Use Probability to Predict

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. According to the experimental probability, is Nikki more likely to get all heads or no heads on the next toss?

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Since it asks for experimental probability use the data in the chart

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Write the probability statement for all heads

Is Nikki more likely to get all heads or no heads on the next toss?

P(all heads) = Number of all heads

Write formula for probability

Total number of tosses

Replace numerator with number of all heads

P(all heads) = 6

Add total number of tosses

80

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Simplify fraction using the calculator

Is Nikki more likely to get all heads or no heads on the next toss?

P(all heads) = Number of all headsTotal number of tosses

P(all heads) = 6 80

P(all heads) = 3 40

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Write the probability statement for no heads

Is Nikki more likely to get all heads or no heads on the next toss?

P(no heads) = Number of no heads

Write formula for probability

Total number of tosses

Replace numerator with number of no heads

P(all heads) = 3

Add total number of tosses

40

P(no heads) = 12 80

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Is Nikki more likely to get all heads or no heads on the next toss?

P(no heads) = Number of no headsTotal number of tosses

P(all heads) = 3 40

P(no heads) = 12 80

Simplify fraction using the calculator

P(no heads) = 3 20

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

1/6

Is Nikki more likely to get all heads or no heads on the next toss?

P(no heads) =

P(all heads) = 3 40

To compare probabilities, must convert to a decimal

3 20

0.075

Make sure to line up the decimals for comparison

0.15

Compare decimals

No heads has a greater probability

Answer: No heads

Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. According to the experimental probability, is Marcus more likely to get all heads or no heads on the next toss?

Answer: all heads 7one head

20two heads

12three heads

6all heads

Number of Tosses

Result

5no heads

1/6

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important?

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

Remember: To do this must multiply the number of outcomes of each event by the other outcomes

2/6

To find the number of outcomes, use the Fundamental Counting Principle

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important?

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

2/6

Each coin that is flipped has 2 possible outcomes

1st Coin

2

2nd Coin

2

3rd Coin

2

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important?

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

2/6

Multiply

1st Coin

2

2nd Coin

2

3rd Coin

2

8Answer:

Add dimensional analysis

possible outcomes

Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. How many possible outcomes are there for tossing four coins if order is important?

Answer: 16 possible outcomes 7one head

20two heads

12three heads

6all heads

Number of Tosses

Result

5no heads

2/6

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

12no heads

30one head

32two heads

6all heads

Number of Tosses

Result

3/6

Remember: theoretical probability is what “might” happen

The experimental (actual) data has nothing to do with theoretical

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Write the probability statement for heads

P( heads) = Number of headsTotal number of outcomes

Write formula for heads

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Replace numerator with number of heads on a coin

P( heads) = Number of headsTotal number of outcomes

P( heads) = 1

Replace denominator with number of sides a coin has

2

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

The probability of each coin being heads will be the same

P( heads) = Number of headsTotal number of outcomes

P( heads) = 1 2

Write probability statement for “all heads”

P(all heads) =

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Multiply the probability of each coin

P( heads) = Number of headsTotal number of outcomes

P( heads) = 1 2

P(all heads) = 1 1 1 2 2 2

P(all heads) = 1 8

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Write the probability statement for no heads

P( no heads) = Number of no headsTotal number of outcomes

Write formula for no heads

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Replace numerator with number of no heads on a coin

P(no heads) = Number of no headsTotal number of outcomes

P(no heads) = 1

Replace denominator with number of sides a coin has

2

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

The probability of each coin being no heads will be the same

P( no heads) = Number of headsTotal number of outcomes

P(no heads) = 1 2

Write probability statement for “all heads”

P(all no heads) =

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Multiply the probability of each coin

P( heads) = Number of headsTotal number of outcomes

P( heads) = 1 2

P(all no heads) = 1 1 1 2 2 2

P(all no heads) = 1 8

Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads?

3/6

Since both probabilities are the same

P( all no heads) = 1 8

P( all heads) = 1 8

Is

no heads? the theoretical probability greater for tossing all heads or

The probabilities have equal chances

Answer:

Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. Is the theoretical probability greater for tossing all heads or no heads? What is the theoretical probability of each?

7one head

20two heads

12three heads

6all heads

Number of Tosses

Result

5no heads

P(all heads) =

P(all no heads) =

Answer:

3/6

The probabilities have equal chances

MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation?

P(stay home) =

4/6

Write the probability statement staying home

What is the experimental probability that an adult planned to stayhome

Write the formula for probability

Number stay home Total Adults

MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation?

P(stay home) =

4/6

Replace numerator with number planning to stay home

What is the experimental probability that an adult planned to stayhome

Number stay home Total Adults

P(stay home) = 560

Replace denominator with total asked

800

MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation?

P(stay home) =

4/6

Simplify with calculator

What is the experimental probability that an adult planned to stayhome

Number stay home Total Adults

P(stay home) = 560 800

P(stay home) =Answer:

MARKETING Five hundred adults were asked whether they were planning to stay home for New Year’s Eve. Of those surveyed, 300 said that they were. What is the experimental probability that an adult planned to stay home for New Year’s Eve?

Answer: P(stay home) =

4/6

Answer: Experimental probability,

wins have already happened

MATH TEAM Over the past three years, the probability

that the school math team would win a meet is Is

this probability experimental or theoretical? Explain.

Experimental: What has happened

Theoretical: What will happen

5/6

“over the past 3 years” refers to what has happened

Answer: Experimental; it is based on actual results.

SPEECH AND DEBATE Over the past three years, the

probability that the school speech and debate team

would win a meet is Is this probability experimental

or theoretical? Explain.

5/6

MATH TEAM Over the past three years, the probability

that the school math team would win a meet is If

the team wants to win 12 more meets in the next 3

years, how many meets should the team enter?

Use a proportion to solve this problem

6/6

Write the probability as the first ratio

Remember: a ratio is a part over the whole

MATH TEAM Over the past three years, the probability

that the school math team would win a meet is If

the team wants to win 12 more meets in the next 3

years, how many meets should the team enter?

6/6

“wants to win” refers to a part of the total wins

Define the variable

Cross multiply to find the value of “x”

3x

Cross multiply

6/6

= 5(12)

Multiply

Ask “what is being done to the variable?”

The variable is being multiplied by 3

Do the inverse on both sides of the equal sign

Answer:

3x

Bring down 3x = 60

6/6

= 5(12)Using a fraction bar, divide both sides by 3

Combine “like” terms

1 x = 20

Use the Identity Property to multiply 1 x

x = 20

Add dimensional analysis

How many meets should the team enter?

meets

SPEECH AND DEBATE Over the past three years, the

probability that the school speech and debate team

would win a meet is If the team wants to win 20

more meets in the next 3 years, how many meets

should the team enter?

Answer: x = 25 meets

*

6/6

Assignment

Lesson 8:6 Experimental Probability 3 - 17 All