11.3 probability in society
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11.3 Probability in Society
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June 05, 2014
11.3 Probability in Society
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June 05, 2014
Theoretical vs. Experimental
Probability
Theory: a set of principles that can be used to explain something.
Experiment: A test under controlled conditions that test a hypothesis.
Given these definitions, how can we define theoretical and experimental probabilities?
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Theoretical vs. Experimental
Probability
Theoretical Probability: The number of favourable outcomes written as a fraction of the total number of possible outcomes.
"What should happen in a perfect world"
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Theoretical vs. Experimental
Probability
Experimental Probability: The probability of an event calculated from experimental results.
"What actually happens once you conduct a trial/experiment"
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Will theoretical probability and experimental probability ever be the
same?
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Assumptions
Before we do any experiment, we have to make assumptions. What is an assumption?
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Assumptions
Coin Flip
What assumptions do we make about a coin before we flip it?
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Assumptions
What if we flip a coin and get 15 heads and no tails.
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Making PredictionsExample
In baseball, a batting average is expressed as a 3 decimal place number. This represents the ratio of total number of hits to the total number of official atbats. For example, if Sam had 12 hits in 40 atbats, his batting average would be 12/40 = 0.30. This average also represents the probability of Sam getting a hit each time he is at bat. That means he will get a hit approximately 30% of the time.
Suppose in the next game, Sam goes up to bat 6 times. How many hits will he get? What assumptions are you making?
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Making Predictions
Example
Ruth wants to determine the most common eye colour of students. All grade 12 students in five of seven high schools in a city recorded their eye colour. A total of 2300 students were surveyed. The results are shown in the table.
Eye Colour Total
Brown 1656
Blue 483
Green 115
Other 46
a. From the results, predict how many of the 7200 students at the local college will have brown eyes.
b. Is your prediction reasonable?
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Biased Sample
A biased sample does not represent the population and can make survey results inaccurate.
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Making Predictions
Example
A youth association surveys its 400 members about their preferred activity. There are 100 members in each of four groups. The activities were chosen from a youth activities resource. The table displays the survey results.
a. What is the probability that a member of any group will choose swimming? Based on this, predict how many of the 400 members will choose swimming.
Group Swimming Rock Climbing
Watching Movies Bowling Total
Red 14 9 40 17 100
Blue 11 19 59 11 100
Green 27 12 57 4 100
Yellow 13 24 44 19 100
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Making Predictions
Example
A youth association surveys its 400 members about their preferred activity. There are 100 members in each of four groups. The activities were chosen from a youth activities resource. The table displays the survey results.
b. What assumptions did you make?
Group Swimming Rock Climbing
Watching Movies Bowling Total
Red 14 9 40 17 100
Blue 11 19 59 11 100
Green 27 12 57 4 100
Yellow 13 24 44 19 100
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Making Predictions
Example
A youth association surveys its 400 members about their preferred activity. There are 100 members in each of four groups. The activities were chosen from a youth activities resource. The table displays the survey results.
c. Based on the survey results, predict the probability that a member will choose swimming.
Group Swimming Rock Climbing
Watching Movies Bowling Total
Red 14 9 40 17 100
Blue 11 19 59 11 100
Green 27 12 57 4 100
Yellow 13 24 44 19 100
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Activity
Roll the Dice