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pch Conditional Probability.pdf

pch Conditional Probability.pdf - Stats post-class handout...

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Stats post-class handout: Conditional Probability Cichello 1 Conditional Probability The textbook can provide you with sufficient information on the basic terminology used in probability problems (See. Ch. 3.1). It will also cover the Probability Postulates (last part of Ch. 3.2). Conditional Probability If you understand the definition and concept of conditional probability well, the rest of this section comes naturally. For example: If you know the conditional probability formula: ) Pr( ) Pr( ) | Pr( B B A B A Then, you can multiply both sides by Pr(B) and you have: ) Pr( ) | Pr( ) Pr( B B A B A This is the multiplication rule. But what does Pr(A|B) mean? It means the probability of event A happening if we know event B happened. NOTE: We always put what we are conditioning on (i.e. the group we are selecting from) on the far right after the “|” symbol. This can be read, “given B” or “conditional on B having happened” or something similar. What is statistical independence? Pr(A|B) = Pr(A) i.e. the probability of event A happening is the same or not event B happened. This can be stated a variety of ways: Pr(A|B) = Pr(A) or ) Pr( ) Pr( ) Pr( B A B A Can you see where the latter formula comes from? Example (with Venn Diagrams) Note: I intentionally use very clear, simple language as this is our first example. There are 150 people in our class. This represents our sample space. There are 60 freshmen in the class, which we shall refer to as F. 20 people in the class are sick with a cold, stomach bug or flu. We will refer to them as S. 10 of the people who are sick are freshman. What is the probability that I pick a freshman if I grab one person at random from the class?
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