math 1105: homework 2 solutions
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Math 1105: Homework 2 Solutions
Part A
7.3
11. An event is a subset of a sample space.
7.4
1. Two events are mutually exclusive if it is impossible for both of them to happen at thesame time. Equivalently, events E and F are mutually exclusive if the intersection E ∩ F is
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the empty set.
2. Union rule for mutually exclusive events: If E and F are mutually exclusive events, thenP (E ∪ F ) = P (E) + P (F ). This is because the event E ∪ F occurs exactly when either Eor F occurs. Ordinarily, summing P (E)+P (F ) would double-count all the outcomes in theintersection E ∩ F ; but since E and F are mutually exclusive, there are no such outcomesto double-count.
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Part B
7.3
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7.4
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45. This is a trick question. Let B be the event that Linda is a bank teller, and let F be theevent that Linda is a feminist. You are given a lot of information indicating that P (F ) isvery high (close to 1). However, the question is: Which is more likely, that Linda is a bankteller (the event B) or that Linda is a bank teller and a feminist (the event B ∩F )? Clearly,if Linda is both a bank teller and a feminist, so that B ∩F is true, then in particular she is abank teller (that is, B is true). In the language of set theory, B ∩ F is a subset of B. ThusP (B ∩ F ) must be less than or equal to P (B). This is true no matter how likely F is.
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7.4
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