Question

ECE 314-Probability and Random Processes, Spring 2019 Homework #1 Due: 02/01/19, at the start of lecture (9:05 am) 1. Suppose that A, B, and C are events such that PlAI-PlB) 03. PC-055, PA n B- 0, PA nBnc]-0.1, and PIAnC]-0.2. For each of the events given below in parts (a)-(d), do the following: i) Write a set expression for the event. (Note that there are multiple ways to write this in many cases.) (i) Evaluate the probability of the event. (Hint: Draw the Venn Diagram. You may then want to identify the probabilities of each of the disjoirnt regions in the diagram before starting the problem.) (a) At least one of the events A, B, or C occurs. (b) Exactly one of A, B, or C occurs. (c) At most one of A, B, or C occurs. (d) C occurs, but neither A nor B occurs 2. Prove the three-set version of the inclusion-exclusion principle: using P(AUB) P(A)+P(B)- Plan B), prove that P(AU BUC) = P(A)+PlB)+P(C)-Plan B)-P(Anc)-P(Bnc1+ P(AnBnc)

Answer 1

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