Theorem 1.8. For a probability function P and any events A and B, A P(A)=1- P(A). B If AC B, then P(A) < P(B). C P(AUB) = P(A) + P(B) = P(ANB). (inclusion-exclusion for two events -

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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just using the definition of probability and the theorem on page 17 of the notes, prove that
for any events A and B,
P (A) + P (B) − 1 ≤ P (A ∩ B) ≤ P (A ∪ B) ≤ P (A) + (B).
(Please label them as “Inquality I”, “First In-
equality”, “Inequality A”, etc.)
Note: You may use Venn diagrams as guides, but a picture is not
a complete proof. give proofs in complete sentences and mathematical
work

Theorem 1.8. For a probability function P and any events A and B,
A P(A)=1- P(A).
B If AC B, then P(A) < P(B).
C P(AUB) = P(A) + P(B) = P(ANB). (inclusion-exclusion for two events
-
Transcribed Image Text:Theorem 1.8. For a probability function P and any events A and B, A P(A)=1- P(A). B If AC B, then P(A) < P(B). C P(AUB) = P(A) + P(B) = P(ANB). (inclusion-exclusion for two events -
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