W2 handout - BUS421 – Week 2 handout(additional...

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Unformatted text preview: BUS421 – Week 2 handout (additional explanations) Bayes' theorem The theorem can be stated in a number of slightly different ways. Essentially, it gives us a way to express, relate, and work with different measures of "conditional probabilities". For example, according to Bayes' theorem, the probability of some uncertain event (say A) happening sometime in the future, given that another event (say B) has already occurred, is ) / ( B A P ) ( ) ( B P B A P ) ( ) ( ) / ( B P A P A B P ) ' ( ) ' / ( ) ( ) / ( ) ( ) / ( A P A B P A P A B P A P A B P Let us assume that there are two events, A and B, and the probability of A happening is 0.80, and the probability of B happening is 0.70. In the Venn diagram format, separately for A and B, we have: We can also describe what we see in the above diagrams as: P(A) = 80/100, P(A') = 20/100 P(B) = 70/100, P(B') = 30/100 [Note that the rectangle is the universal set which includes everything. A' is the complement of set A, and is everything that is in the universal set but not in the set A.] The two events that we are interested in can occur at the same time and assume that the probability of A and B happening at the same time is 0.60. Putting this into a Venn diagram, we can show the different event probabilities as follows: We can also describe what we see in the above diagram as: P(A B) = 60/100 P(A B') = 20/100 P(A' B) = 10/100 P(A' B')...
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W2 handout - BUS421 – Week 2 handout(additional...

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