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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 Spring '08
 MARTIN
 Probability, Probability theory

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