PROBABILITY

Definitions

An experiment is a situation involving chance or probability that leads to results called outcomes

An outcome is the result of a single trial of an experiment

An event is one or more outcomes of an experiment

Probability is the measure of how likely an event is

Examples of Definitions:

A spinner has 4 equal sections colored yellow, blue, green, and red.What are the chances of landing on blue?

•The experiment is spinning the spinner

•The possible outcomes are landing on yellow, blue, red, or green

•One event of this experiment is landing on blue

•The probability of landing on blue is one-fourth

More on Probability Probability is a number from 0 to 1 that tells

you how likely something is to happen. Probability can be either theoretical or

experimental.

ProbabilityTHEORETICAL

Theoretical probability can be found without doing an experiment. When each event is equally likely to happen.

EXPERIMENTAL

Experimental probability is found by repeating an experiment and observing the outcomes.

Theoretical Probability

The probability of an event (A) is the number of ways event (A) can occur divided by the total number of possible outcomes.

P(A) =The number of outcomes where A can occur The total number of possible outcomes

So, using the spinner experiment, what is the probability of landing on blue?

P(blue) = 1 4

THEORETICAL PROBABILITY

I have a quarterMy quarter has a heads side and a tails side

Since my quarter has only 2 sides, there are only 2 possible outcomes when I flip it. It will either land on heads, or tails

HEADS

TAILS

THEORETICAL PROBABILITY

When I flip my coin, the probability that my coin will land on heads is 1 in 2

What is the probability that my coin will land on tails??

HEADS

TAILS

Theoretical Probability

Right!!! There is a 1 in 2 probability that my coin will land on tails!!!

HEADS

TAILS

A probability of 1 in 2 can be written in three ways:

•As a fraction: ½•As a decimal: .50

•As a percent: 50%

Theoretical probability

When I spin this spinner, I have a 1 in 4 chance of landing on the section with the red A in it.

A

A

A

A

A 1 in 4 chance can be written 3 ways:

As a fraction: ¼ As a decimal: .25 As a percent: 25%

A

A

A

A

Theoretical Probability

The probability is equally likely when each section is the same size

I am going to take 1 marble from the bag. What is the probability that I will pick

out a red marble?

Theoretical Probability

I have three marbles in a bag.

1 marble is red

1 marble is blue

1 marble is green

Theoretical Probability Since there are three

marbles and only one is red, I have a 1 in 3 chance of picking out a red marble.

I can write this in three ways:

As a fraction: 1/3 As a decimal: .33 As a percent: 33%

Experimental Probability

Experimental probability is found by repeating an experiment and observing the outcomes.

Experimental Probability

The probability based on the outcomes you obtained in an experiment.

P(A) = Number of times event A occurs in the experiment Total number of trials

Experimental Probability

In our spinner experiment, if we spin 10 timesand the outcomes were:

Blue 4

Red 3

Green 2

Yellow 1

P(blue) = 4 or 2 10 5

Experimental Probability Remember the bag of marbles? The bag has only 1 red, 1 green, and

1 blue marble in it. There are a total of 3 marbles in the

bag. Theoretical Probability says there is a

1 in 3 chance of selecting a red, a green or a blue marble.

Experimental Probability

Draw 1 marble from the bag.

Marble number red blue green

1 123456

It is a red marble.

Record the outcome on the tally sheet

Experimental Probability Put the red marble back in the bag and

draw again. This time your drew a green marble. Record this outcome on the tally sheet.

Marble number red blue green

1 12 134

Experimental Probability Place the green marble back in the bag. Continue drawing marbles and recording

outcomes until you have drawn 6 times. (remember to place each marble back in the bag before drawing again.)

Experimental Probability After 6 draws your

chart will look similar to this.

Look at the red column. Of our 6 draws, we

selected a red marble 2 times.

Marble number red blue green

1 12 13 14 15 16 1

Total 2 1 3

Experimental Probability The experimental

probability of drawing a red marble was 2 in 6.

This can be expressed as a fraction: 2/6 or 1/3 a decimal : .33 or a percentage: 33%

Marble number red blue green

1 12 13 14 15 16 1

Total 2 1 3

Experimental Probability Notice the

Experimental Probability of drawing a red, blue or green marble.

Marble number red blue green

1 12 13 14 15 16 1

Total 2 1 3

Exp. Prob.

2/6 or 1/3 1/6

3/6 or 1/2

Comparing Experimental and Theoretical Probability

Look at the chart at the right.

Is the experimental probability always the same as the theoretical probability?

red blue greenExp. Prob. 1/3 1/6 1/2Theo. Prob. 1/3 1/3 1/3

Comparing Experimental and Theoretical Probability

In this experiment, the experimental and theoretical probabilities of selecting a red marble are equal.

red blue greenExp. Prob. 1/3 1/6 1/2Theo. Prob. 1/3 1/3 1/3

Comparing Experimental and Theoretical Probability

The experimental probability of selecting a blue marble is less than the theoretical probability.

The experimental probability of selecting a green marble is greater than the theoretical probability.

red blue greenExp. Prob. 1/3 1/6 1/2Theo. Prob. 1/3 1/3 1/3

Probability Review

Theoretical (can be found without doing an experiment)

Experimental (can be found by repeating an experiment and recording outcomes.)

There are 2 types of probability:

Probability is a number from 0 to 1 that tells you how likely something is to happen.

Probability Review

Probability can be expressed as a fraction, a decimal or a percentage.

Probability fraction decimal percent1 in 2 1/2 0.50 50%

1 in 3 1/3 0.33 33%

1 in 4 1/4 0.25 25%

Chances Are…

You can do it!

Activity #1

1,1

1,2 2,1

1,3 3,1 2,2

2,3 3,2 1,4 4,1

2,4 4,2 1,5 5,1 3,3

3,4 4,3 2,5 5,2 1,6 6,1

2,6 6,2 3,5 5,3 4,4

3,6 6,3 4,5 5,4

4,6 6,4 5,5

5,6 6,5

6,6

What is the probability of rolling an even numbered sum?

A sum smaller than 4?

A square number sum?

What is the probability of rolling an even number sum?

A number sum smaller than 4?

A square number sum?

Write like a mathematician in your journal,

showing these questions and answers.

Click mouse to see answers

What is the probability of rolling an even number sum?

P (even number sum) = 18/36 or 1/2

A number sum smaller than 4?

P (number sum smaller than 4) = 3/36 or 1/12

A square number sum?

P (square number sum)= 8/36 or 4/9

End of Activity

Chances Are…

You can do it!

Activity #3

DRAWING DRAWING MARBLESMARBLESA jar contains two red marbles, three blue marbles, and four green marbles. Niki draws one marble from the jar, and then Tom draws a marble from those remaining. What is the probability that Niki draws a green marble AND Tom draws a blue marble? Express your answer as a common fraction.

# of total possible outcomes

# of desired outcomes

Niki has a 4/9 chance of drawing a green and

Tom has a 3/8 chance of drawing a blue.

# of total possible outcomes

# of desired outcomes

Niki has a 4/9 chance of drawing a green and

Tom has a 3/8 chance of drawing a blue.

4/9 x 3/8 =

12/72 or 1/6There is a 1/6 chance that Niki will draw a green marble AND Tom will draw a blue marble. End of Activity