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Unformatted text preview: isjoint, then P (A) = 0 or P (B ) = 0.
Since we know, that P (A ∩ B ) = P (A)P (B ) the statement follows directly, if we also assume, that the
events are disjoint, i.e. P (A ∩ B ) = 0
(c) If they are exhaustive (i.e. A ∪ B = Ω), then P (A) = 1 or P (B ) = 1.
From 1 = P (A ∪ B ) we get,
1 = P (A ∪ B ) = 1 − P (A ∩ B ) = 1 − P (A) · P (B ) Therefore
P (A) · P (B ) = 0,
which implies that either P (A) = 0 or P (B ) = 0. Then either P (A) = 1 or P (B ) = 1.
(4 points) 2 Bayes’ Theorem (a) Suppose that a barrel contains many small plastic eggs. Some eggs are painted red and some are painted
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This homework help was uploaded on 03/11/2014 for the course STAT 330 taught by Professor Staff during the Spring '08 term at Iowa State.
- Spring '08