Since we know that p a b p ap b the statement follows

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 blue. 4...
View Full Document

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.

Ask a homework question - tutors are online