1.20 Theoretical Probability.notebook
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Theoretical Probability
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Warm Up
Discuss with the person next to you and be prepared to share your answers.
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DefinitionsTheoretical probability• Probability based on analysis of all possible outcomes• Also called classical probability
Sample Space• Collection of all possible outcomes• Sometimes called a sample set
Event• Set of outcomes that have a common characteristic
Complement• Set of outcomes not included in an event
Odds in Favour• Ratio of the probability that an event will happen to the probability that it will not
Odds Against• Ratio of the probability that an event will not happen to the probability that it will
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Instead of using a sample space diagram you can also use a tree diagram or Venn diagram to help organise the outcomes. You can also use set notation (similar to domain and range).
For example trying to find the probability of rolling an even number on a die...
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Sometimes you need to know the probability that one event happens compared to all others. If one event is A then event A' (A prime) is all the possible outcomes not in A. This is also known as the complement of A. Because the sum of all probabilities in a sample space must equal one, there is a useful relationship between P(A) and P(A').
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a) The set of all possible outcomes is the sample space. An event is a set of outcomes in the sample space that have a common characteristic. Then, the probability of an event A happening is the number of outcomes in that subset divided by the total number of outcomes in the sample space.
SA
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S = {1 20} A = {Prime < 20}
P(A) = = = 820
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n(A)n(S)
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a) The complement of an event is the set of possible outcomes not included in an event.
b) The weather forecast is predicting rain this afternoon. It says there is a 70% chance. What is the probability of it not raining this afternoon?
P(R') = 1 P(R)P(R') = 1 0.70P(R') = 0.30P(R') = 30%
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a) Odds in favour of an event is a ratio of the probability that an event will happen to the probability that it will not happen.
b) Odds against an event is a ratio of the probability that an event will not happen to the probability that it will happen.
c) They are similar in that they use the same probabilities. They are different in that the order is important.
HomeworkMHR Page 24 #s 1 10