Question

EE3180 Make sure to read all questions carefully and answer them completely, To ensure the potential of receiving partial credit, it is in your best interests to show sufficient work which shows your reasoning in finding a solution. Numerical answers can be given as either rational numbers or as decimal approximations which are accurate to at least three significant digits. 1. In a class of 100 students, suppose that there are 40 who are fans of the Detroit Lions, 20 who are fans of the Green Bay Packers, and 8 who are fans of both teams. If we randomly pick a student, let A denote the event that they are a Lions fan, and let B denote the event that they are a Packers fan. (a) Give a verbal description of the event ABe. What is the probability of this event? (b) Calculate P(AU B). (c) Calculate P(AB). (d) Are A and B independent events? You must justify your answer to receive any credit. 14 2. For some events A, B in a sample space Ω, suppose that A u B = B, what relationship does this imply about A and B? Draw a Venn diagram to "prove" your claim.

Answer 1

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