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Lecture7

# 4 notes example 20 independence and law of total

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Unformatted text preview: 7.4 Notes Example 20 Independence and Law of Total Probability Notes The independence of the events A and B implies that the following are independent: 1 Ac and B 2 A and B c 3 Ac and B c Independence Law of Total Probability 7.5 Example 20 Independence and Law of Total Probability Solution. Independence Law of Total Probability 7.6 Notes Independence for more than two events Independence and Law of Total Probability Notes Consider more than two events A1 , A2 , · · · , Ak , we have two types of independence: Pairwise independent P(Ai ∩ Aj ) = P(Ai ) × P(Aj ) i , j ∈ 1, 2, · · · , k i = j Independence Law of Total Probability Mutually independent P(Ak1 ∩ Ak2 ∩ · · · ∩ Akn ) = P(Ak1 ) × P(Ak2 ) × · · · × P(Akn ) ki , kj ∈ 1, 2, · · · , k ki = kj 1 ≤ n ≤ k 7.7 Example 21 Chris and his roommates each have a car. Julia’s Mercedes SLK works with probability .98, Alex’s Mercielago Diablo works with probability .91, and Chris’ 1987 GMC Jimmy works with probability .24. Ass...
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