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NotesAug30 - Conditional probabilities have very similar...

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Conditional probabilities have very similar prop- erties to the usual “unconditional” probabili- ties. For a fixed event B with P ( B ) > 0, 1. For every event A , 0 P ( A | B ) 1. 2. For the sample space Ω, P | B ) = 1. 3. For disjoint (mutually exclusive) events A 1 , A 2 , . . . , ... P ( n i =1 A i | B ) = n X i =1 P ( A i | B ) for every n = 1 , 2 , . . . , .
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Conditional probabilities can be conditioned “even further” . With 3 events, A , B and C , P ( A | B, C ) = P ( A B | C ) P ( B | C ) .
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Example : Customers purchasing a full set of tires at a particular store can buy either tires made in the United States or tires made else- where. 90% of customers purchasing tires made in the United States have tires balanced immediately 60% of customers purchasing tires made in the United States request immediately both tire balancing and front end alignment. Given that a customer has purchased a full set of tires made in the United States and re- quested tire balancing, what is the probability that this customer has also requested a front end alignment?
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