Lecture7

# What is the probability that at least 1 car works

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Unformatted text preview: ume all cars work independently of on another. What is the probability that at least 1 car works? Independence and Law of Total Probability Independence Law of Total Probability 7.8 Notes Example 21: Julia’s SLK Independence and Law of Total Probability Notes Independence Law of Total Probability 7.9 Example 21: Alex’s Diablo Independence and Law of Total Probability Independence Law of Total Probability 7.10 Notes Example 21: Chris’ 1987 Jimmy Independence and Law of Total Probability Notes Independence Law of Total Probability 7.11 Example 21 Independence and Law of Total Probability Solution. Independence Law of Total Probability 7.12 Notes Independence and Law of Total Probability Law of total probability Notes Recall the law of partitions Let A1 , A2 , · · · , Ak form a partition of Ω. Then, for all events B , k P(Ai ∩ B ) P(B ) = i =1 Independence Law of Total Probability By applying the general multiplication rule, we have the law of total probability k P(B |Ai ) × P(Ai ) P(B ) = i =1 7.13 Example 22 Acme Consumer Goods sells three brands...
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