Olmedo Probability

Probability

Experimental Probability and

Theoretical Probability and Simulations

Basic Concepts

About Probability

It is the

​set of all possible outcomes of an event.

When you roll a die, you can ONLY land on the numbers

1 through 6. So the sample space is {1, 2, 3, 4, 5, 6}.

Sample Space

Match

Match the following to their sample spaces.

{red, blue, yellow, green}

{heads, tails}

{R, O, Y, G, Blu, Blk, Brn, P)

{K of hearts, K of spades, K of clubs, K or diamonds}

• {red, blue, yellow, green}

• {heads, tails}

• {R, O, Y, G, Blu, Blk, Brn, P)

• {K of hearts, K of spades, K of clubs, K or diamonds}

In the next few slides, you'll be asked some simple questions about the likelihood of an event when you roll a die like the one shown in the picture.

​

​Rolling a die

Multiple Choice

How many sides does a standard fair die have?

Fair means all sides have an equal chance of being rolled.

• 3

• 4

• 5

• 6

• More than 6

Match

Imagine rolling ONE standard die. Many outcomes are possible.

Match the following events to their likelihood of them happening.

• Rolling a number from 1 to 6

• Rolling a number greater than 4

• Rolling an odd number

• Rolling a 7

• Rolling a number other than 6

6 out of 6

2 out of 6

3 out of 6

0 out of 6

5 out of 6

• 6 out of 6

• 2 out of 6

• 3 out of 6

• 0 out of 6

• 5 out of 6

Match

Probabilities can be expressed as fractions.

Match the following events to their likelihood of them happening.

• Rolling a number from 1 to 6

• Rolling a number greater than 4

• Rolling an odd number

• Rolling a 7

• Rolling a number other than 6

6/6 or 1

1/3

1/2

0/6 or 0

5/6

• 6/6 or 1

• 1/3

• 1/2

• 0/6 or 0

• 5/6

Match

Probabilities can be expressed as decimals.

Match the following events to their likelihood of them happening.

• Rolling a number from 1 to 6

• Rolling a number less than 3

• Rolling an even number

• Rolling a 12

• Rolling a number other than 6

1.00

about 0.33

0.50

0.00

about 0.83

• 1.00

• about 0.33

• 0.50

• 0.00

• about 0.83

Match

Probabilities can be expressed as percents.

Match the following events to their likelihood of them happening.

• Rolling a number from 1 to 6

• Rolling a 2 or a 4

• Rolling a number less than 4

• Rolling an 11

• Rolling a number other than 1

100%

about 33%

50%

0%

about 83%

• 100%

• about 33%

• 50%

• 0%

• about 83%

It is written as P(event) and is a measure of the likelihood of an event happening. Probabilities are always values between 0 and 1, inclusive.

The Probability of an Event

Dropdown

You roll a standard die. The probability of:

A) rolling a number from 1 to 6 is ​

Select answer

.

B) rolling a 2 or a 4 is ​

Select answer

.

C) rolling an even number is ​

Select answer

.

D) of rolling a 9 is ​

Select answer

.

E) rolling a number other than 6 is ​

Select answer

.

Multiple Select

You spin the spinner on the left one time.

Which statements are true regarding P(primary color) - the likelihood of landing on a primary color?

• P(primary color) = 75%

• P(primary color) = 25%

• P(primary color) = 3/4

• P(primary color) is certain.

• P(primary color) is likely.

​It is the set of all outcomes in the sample space that are NOT included in the event. For example, in the event of rolling a number greater than 4 on a standard die, the COMPLEMENT is rolling a number less than or equal to 4 - or rolling 1, 2, 3, or 4.

P(number greater than 4) + P(number less than or equal to 4) = 1 or 100%

0.333... + 0.666... = 1

2/6 + 4/6 = 1

33.3% + 66.7% = 1

The Complement of an Event

Multiple Choice

A spinner has 3 equal sections that are red, white, and blue.

What is the probability of NOT landing on blue?

• 1/3

• 2/3

Multiple Choice

A spinner has 5 equal sections numbered 1 through 5.

What is the probability of NOT landing on 4?

• 4/5

• 1/5

Multiple Choice

There are 4 queens in a standard deck of 52 poker cards. You pick a card at random.

What is the probability of NOT drawing a queen?

• 12/13

• 1/13

Events that include two or more simple events such as rolling a die and flipping a coin OR rolling a die and spinning a spinner.

Examples of Compound Events

• rolling a die

• flipping a coin

• spinning a spinner

• choosing a card from a deck

Examples of Simple Events

Compound Events vs Simple Events

Experimental Probability

Always based on events that have already occurred.

The experimental probability of an event is the ratio of the number of times an event occurs to the total number of trials.

Experimental Probability of

Simple Events

Donny has a bag of marbles. ​He pulled out a marble, recorded the color, and put it back in the bag. He repeated this process many times. Here are his results.

Use these results to answer the questions on the next few slides.

Example: Bag of Marbles

Fill in the Blank

The table shows the results of trials from Donny's experiment. How many trials did he conduct? __

Drag and Drop

The table shows the results of trials from Donny's experiment.

What's the experimental probability (as a fraction) of drawing each color?

Red: ​​

Placeholder

Blue: ​

Placeholder

Green: ​

Placeholder

Yellow: ​

Placeholder

Drag these tiles and drop them in the correct blank above

12/50

10/50

15/50

13/50

50/50

25/50

Drag and Drop

The table shows the results of trials from Donny's experiment.

What's the experimental probability (as a percent) of drawing each color?

Red: ​

Placeholder

Blue: ​

Placeholder

Green: ​ ​

Placeholder

Yellow: ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

24%

20%

30%

26%

100%

25%

Drag and Drop

The table shows the results of trials from Donny's experiment.

Use his results to predict how many times each color will be drawn in the next 60 trials. (Rounding will be necessary.)

Red

Placeholder

Blue

Placeholder

Green

Placeholder

Yellow ​

Placeholder

Drag these tiles and drop them in the correct blank above

14

12

18

16

13

15

17

19

20

11

Experimental Probability of Compound Events

A parking lot attendant kept track of the types and colors of the vehicles that parked in a parking lot.

Use the data in the table to answer the questions in the next few slides.

Example: Parking Lot

Fill in the Blank

The parking lot attendant recorded the type and color of each vehicle that was parked in the lot.

How many cars did he track? __

Multiple Choice

Based on the results of the paring lot attendant, what is the experimental probability that the next vehicle that parks in the lot will be a black car?

• 14%

• 6%

• 19%

• 13%

• None of these

Multiple Choice

Based on the results of the paring lot attendant, what is the experimental probability that the next vehicle that parks in the lot will be a blue van?

• 3%

• 6%

• 1%

• 8%

• None of these

Multiple Choice

Based on the results of the paring lot attendant, what is the experimental probability that the next vehicle that parks in the lot will be a blue OR red SUV?

• 3%

• 8%

• 5%

• 4%

• None of these

Making Predictions with

Experimental Probability

Multiple Choice

Based on the results of the parking lot attendant, if 20 more vehicles park in the lot, about how many can be predicted to be white cars? Rounding may be necessary.

• 10

• 7

• 5

• 8

• 4

Multiple Choice

Based on the results of the parking lot attendant, on average, what percent of the vehicles parked in the lot are white vehicles?

• 4

• 18

• 30

• 8

• 22

Multiple Choice

Based on the results of the parking lot attendant, on average, 30% of the vehicles in the lot are white. If there are 550 spaces in the lot and all of the spaces are occupied by a vehicle, about how many vehicles would be white?

• 165

• 180

• 120

• 200

• None of these

Theoretical Probability

Takes into account all the possible outcomes. All possible outcomes are EQUALLY LIKELY.

The theoretical probability of an event is the ratio of the number of ways an event can occur to the total number of equally likely outcomes.

Theoretical

Probability of

Simple Events

A bag contains 8 red marbles, 10 blue marbles, and 2 yellow marbles.

Use this information to answer the questions on the next few slides.

Example: Bag of Marbles

Dropdown

A bag contains 8 red marbles, 10 blue marbles, and 2 yellow marbles.

One marble is chosen at random and then placed back into the bag before each trial.

The probability of choosing a red marble is ​

Select answer

%.

The probability of choosing a blue marble is​ ​

Select answer

%.

The probability of choosing a yellow marble is ​

Select answer

%.

Multiple Choice

A bag has 26 tiles. Each tile is marked with one of the letters of the alphabet. What is the probability that when you draw a tile from the bag it will be a vowel?

• 5/26

• 5/21

• 21/26

• 1/5

• None of these

Dropdown

A standard deck of cards is shown.

The probability of drawing a black card is ​

Select answer

.

The probability of drawing a heart is ​

Select answer

.

The probability of drawing a queen is ​

Select answer

.

The probability of drawing the ace of spades is ​

Select answer

.

Theoretical

Probability of Compound Events

Solution:

There are 12 possible outcomes.

So, the probability of choosing Turkey & Swiss on White is 1/12 or about 8%.

Example: The Deli

Match

Match the following events to their probabilities.

• P(sandwich containing Swiss)

• P(ham sandwich)

• P(NOT chicken)

• P(NOT turkey and cheddar)

• P(wheat, ham, & cheddar)

50%

33.3%

66.7%

83.3%

8%

• 50%

• 33.3%

• 66.7%

• 83.3%

• 8%

Fill in the Blank

The small, local ice cream shop has:

5 ice cream flavors,

3 types of toppings,

served in cup or cone

How many different ways can you select 1 flavor, 1 topping, and 1 container?

Making Predictions with

Theoretical

Probability

Multiple Choice

A spinner has 6 equal sections as shown.

If Bob spins the wheel 72 times, it can be predicted that he will land on the number 4 __ times.

• 18

• 24

• 12

• 36

Multiple Choice

A spinner has 6 equal sections as shown.

If Bob spins the wheel 72 times, it can be predicted that he will land on either the number 4 OR 5 __ times.

• 18

• 24

• 12

• 36

Multiple Choice

Karla has three standard dice - numbered 1 through 6. She will roll each die one time.

What is the probability that all 3 dice will land on an odd number?

[HINT: Multiply the individual probabilities of each die.]

• 1/2

• 1/6

• 1/3

• 1/8

Drag and Drop

A bag contains flavored lollipops. A lollipop will be selected at random from the bag.

What is the probability in decimal form - rounded to nearest 1/100 - that the selected lollipop will be:

A) either cherry OR watermelon: ​​

Placeholder

B) neither grape NOR cherry: ​

Placeholder

Drag these tiles and drop them in the correct blank above

0.4

.55

Extra practice problems

Multiple Choice

A student will spin two different spinners in an experiment. The tree diagram shows the possible outcomes.

How many outcomes of one number and one letter are possible?

• 3

• 6

• 9

• 12

Multiple Select

A student will spin two different spinners in an experiment. The tree diagram shows the possible outcomes.

Which of the following are possible outcomes?

• 1R

• 2T

• 3Z

• 2S

• 4Z

Multiple Select

James tossed a coin 3 times. Which tree diagrams DO NOT show all the possible outcomes of the coin landing heads up or tails up?

Match

Match the following.

• P(9)

• P(NOT 9)

• P(greater than 10)

• P(NOT greater than 10)

• P(20)

1/8

7/8

1/4

3/4

0/8

• 1/8

• 7/8

• 1/4

• 3/4

• 0/8