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Grade 8:  The Learning Equation Math

42.01 Exploring Probability

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Chance & Uncertainty

Refresher pp 86-7

Learning Outcomes:

The student will:

  • use computer simulations and other simulations to solve probablility and data collection problems.

 

Experimental and Theoretical Probability for Coins

Experiment:  Toss a coin 20 times using the virtual coin provided. Does the experimental probability have to match the theoretical probability?

The theoretical probability of the event is the fraction:

# ways the event can occur
total possible outcomes
 

The experimental probability for equally likely events is the fraction:

# favourable outcomes
total outcomes
 

In the Experiment, the theoretical probability of the event that heads comes up is:

P(H) =

1/2

= 0.5 = 50%
P(T) = 1/2 = 0.5 = 50%

The experimental probability for equally likely events is the fraction:

# favourable outcomes
total outcomes

In the Experiment, if heads comes up 13 of 20 times, the experimental probability of the event that heads comes up is:

P(H) = 13/100

= 0.65 = 65%

 

 

 

Colour Spinner

The theoretical probability of the event is the fraction:

# ways the event can occur
total possible outcomes

The theoretical probability of red is 1/5 or 20%.

The experimental probability for red:

          # red         
total outcomes(spin)

Click the green button 100 times.  Does the experimental probability match the theoretical probability.

 

 

Experimental and Theoretical Probability for 2 Di

Click on the green button below. The total for the roll is a favorable outcome for the number rolled. Rolling dice produces data for experimental probability.

There are 36 possible outcomes each time two dice are thrown. Study the pattern of the animation below.

Virtual dice for generating experimental and theoretical probability data.

Experiment:  Toss the dice 100 times. If 12 comes up 10 times, what is the experimental probability.

The theoretical probability of the event is the fraction:

# ways the event can occur
total possible outcomes
 

The experimental probability for equally likely events is the fraction:

# favourable outcomes
total outcomes
 
Look at the chart above. The theoretical probability of the event that 12 comes up is:

P(12) = 1/36 = 0.028 = 2.8%

If  in this experiment, 12 is rolled 3 times, the experimental probability of the event that twelves comes up is:

P(12) = 3/100 = 0.03 = 3%

 

Other sites show the theoretical probability and or experimental probability of rolling particular numbers when two dice are rolled.

Probability:   What are Your Chances?

Site 1

 

 

More Rolling Dice

Choose to roll one die or two dice.   Click on an arrow beside the run button to increase or decrease the number of trials.   The help button that has a more detailed explanation of how to use this applet.

java source code files downloaded from:  http://www.journey.sunysb.edu/projectjava/lisa1998/prob/home.html

 

Monte Carlo

 

Review:

Ken White's Coin Flipping Page

Crazy Choices Game

 

Enrichment:

 

 

Key Terms:

theoretical probability, experimental probability, simulation, favourable outcome, possible outcome, sector, tree diagram

 

Prerequisite Skills:

Exploring Probability:  Grade 7 Lesson 42.01

Exploring Probability:  Grade 7 Lesson 42.01

Probability:  Grade 7 Lesson 42.02

Exploring Probability:  Grade 7 Lesson 42.01

Monte Carlo Simulations:  Grade 7 Lesson 42.03

 

 

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Comments to:  Jim Reed

Started September, 1998. Copyright © 1999, 2000