diff --git a/source/ch-Probability.ptx b/source/ch-Probability.ptx index f93ac04..57fa8bf 100644 --- a/source/ch-Probability.ptx +++ b/source/ch-Probability.ptx @@ -1,46 +1,115 @@ - Probability Theory + Probability Theory - -

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- Set Theory +
+ Set Theory -

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+ Consider the sets A = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, B = \{2, 4, 9, 10, 12, 14, 19\}, and C = \{9, 10, 11, 14, 16, 17, 20\}, which are all subsets of \Omega = \{1, 2, 3, \dotsc, 20\}. +

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+ Find A - (B \cap C). +

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+ \{1, 2, 3, 4, 5, 6, 7, 8\} +

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- Definition of Probability + + +

+ Find |A|, |B|, |C|, |A\cup B|, |A \cap B|, |B\cap C|, |A\cap C|, and |A\cup B\cup C|. + Is it true that the size of the union of sets is equal to the sum of the sizes of the individual sets? +

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+ |A| = 10, |B| = 7, |C| = 7, |A \cup B| = 13, |A \cap B| = 4, |B\cap C| = 3, |A\cap C| = 2, |A\cup B\cup C| = 17. In particular, note that |A\cup B| = 13 \neq 10 + 7 = |A| + |B|, so it is not true in general that the size of the union of sets is the sum of the sizes of the individual sets. +

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+ Find A^c and (A\cup B)^c. +

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+ A^c = \{11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}, (A\cup B)^c = \{11, 13, 15, 16, 17, 18, 20\}. +

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+ Suppose we roll a 6-sided die two times. List the set of all possible results. [Note: the result (2, 4)---rolling a 2 and then a 4---is different from the result (4, 2)---rolling a 4 and then a 2.] +

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+ Suppose we flip a coin two times. List the set of all possible results. What about flipping three times? Four times? If we flip the coin 10 times, how many possible results will there be? +

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+ If we roll a 6-sided die ten times, how many possible results will there be? +

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+ Definition of Probability -
- Conditional Probability - -

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- Independent Events - -

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+ Conditional Probability +

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+ Independent Events +

+ Text of section. +

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