ProbabilityProbability

ProbabilityProbability

The ratio of favorable outcomes to The ratio of favorable outcomes to possible outcomes, or in other words possible outcomes, or in other words the likelihood (or chance) that the likelihood (or chance) that something will happensomething will happen

Can be represented as a fraction Can be represented as a fraction (ratio), percent, or decimal(ratio), percent, or decimal

2 Types:2 Types:– TheoreticalTheoretical– ExperimentalExperimental

ProbabilityProbability

Theoretical

Experimental

Theoretical ProbabilityTheoretical Probability

Determined through Determined through mathematical meansmathematical means

Example: What is the probability Example: What is the probability of obtaining tails when flipping a of obtaining tails when flipping a coin?coin?

Citation (MLA)Discovering Math: Probability (Grades 6-8). Discovery Channel School. 2006.unitedstreaming. 3 June 2008<http://streaming.discoveryeducation.com/>

Visit Visit http://www.unitedstreaming.com and view a video segment from and view a video segment from the video the video Discovering Math: Probability (Grades 6-8) called Example 2: Multiple called Example 2: Multiple Events--Number CubesEvents--Number Cubes

Experimental Experimental ProbabilityProbability Obtained through experiments, Obtained through experiments,

simulations, or datasimulations, or data

Example: Flip a coin 50 times, Example: Flip a coin 50 times, record the number of times tails record the number of times tails is obtained, and determine the is obtained, and determine the probability of obtaining tails probability of obtaining tails based on the based on the experiment.experiment.

Citation (MLA)Discovering Math: Probability (Grades 6-8). Discovery Channel School. 2006.unitedstreaming. 3 June 2008<http://streaming.discoveryeducation.com/>

Visit Visit http://www.unitedstreaming.com and and view a video segment from the video view a video segment from the video Discovering Math: Probability Discovering Math: Probability (Grades 6-8) called Example 1: (Grades 6-8) called Example 1: Historical Probability—Basketball Historical Probability—Basketball Free ThrowsFree Throws

DifferencesDifferences

What would make theoretical What would make theoretical probabilities and experimental probabilities and experimental probabilities differ?probabilities differ?

What needs to be done to bring What needs to be done to bring an experimental probability closer an experimental probability closer to a theoretical probability?to a theoretical probability?

Experimental Probability Experimental Probability ExamplesExamples

Susie kicked corner kicks at soccer Susie kicked corner kicks at soccer practice. Out of her 100 attempts, practice. Out of her 100 attempts, her experimental probability of her experimental probability of getting a goal was 55%. How getting a goal was 55%. How many goals did she make?many goals did she make?

Answer 1

Based on the data below, what is the Based on the data below, what is the experimental probability that a student experimental probability that a student from this school received an overall from this school received an overall score of a C for the first 9 weeks?score of a C for the first 9 weeks?

Student’s Overall Scores for the first 9 Weeks of the School YearStudent’s Overall Scores for the first 9 Weeks of the School Year

Class Red Class Red Class Blue Class Blue Class Orange Class Orange Class Green Class Green

AA 14% 14% 20% 20% 18% 18% 10% 10%

B B 22% 22% 24% 24% 20% 20% 18% 18%

CC 36% 36% 41% 41% 32% 32% 44% 44%

D D 18% 18% 10% 10% 22% 22% 16% 16%

F F 10% 10% 5% 5% 8% 8% 12%12%

Answer 2

The results of rolling a six-sided die The results of rolling a six-sided die 140 times are given below.140 times are given below.

Results from Rolling a Die 140 TimesResults from Rolling a Die 140 TimesNumber on dieNumber on die 11 22 33 44 55 66No. of OccurrencesNo. of Occurrences 2020 2121 2424 2121 2626

2828

a.) Find the theoretical probability of a.) Find the theoretical probability of rolling a 4 on a six-sided die.rolling a 4 on a six-sided die.

b.) Find the experimental probability b.) Find the experimental probability based on the given data of based on the given data of

rolling a 4 rolling a 4 on a six-sided die.on a six-sided die.Answer 3

Let’s conduct our own simulations Let’s conduct our own simulations and find the respective and find the respective probabilities.probabilities.

Simulation Time!

The EndThe End

Answer 1Answer 1

5555

Next Example

Answer 2Answer 2

153/400 or about 38%153/400 or about 38%

Next Example

Answer 3Answer 3

a.) 1/6a.) 1/6 b.) 21/140 = 3/20 or 15%b.) 21/140 = 3/20 or 15%

SimulationSlide