probability definitions an experiment is a situation involving chance or probability that leads to...
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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