Math 245 Written Homework 4 Due May 2nd Name: 1. Suppose in an office of 80 people, 50 put creamer in their coffee and 40 take their coffee with sugar. 30 people like both creamer and sugar in their coffee. (a) Draw a Venn Diagram for this situation. (b) Given that someone likes creamer in their coffee, what is the probability they will also have sugar? (c) Are the events C = \"person likes creamer in their coffee\" and S = \"person likes sugar in their coffee\" independent? Why or why not? 1 2. An experiment consists of flipping coins. Let E be the event \"both H and T occur\" and let F be the event \"at least 1 H\". Find out whether or not the E and F are independent by finding P (E F ) and P (E) P (F ) and comparing the results. (a) The coin is flipped 3 times. (b) The coin is flipped 4 times. 2 3. Given a sample space S with n(S) = 100, tell whether each pair of events are independent, mutually exclusive, both or neither: (a) E and F where n(E) = 60, n(F ) = 40, n(E F ) = 0 (b) A and B where n(A) = 50, n(B) = 50, n(A B) = 25 (c) C and D where n(C) = 0, n(D) = 20, n(C D) = 0 (d) G and H where n(G) = 30, n(H) = 50, n(G H) = 20 3