Econ 210 Spring 2009 Problem Set 1 - Solutions

Econ 210 Spring 2009 Problem Set 1 - Solutions - Econ 210...

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Econ 210 Spring Quarter 2009 Problem Set 1 - Solutions Solve the following Problems. Show your work. 1. A balanced coin is tossed three times. Denote H=heads, T=Tails, i.e. HHT stands for heads in the first 2 tries and tails in the third. a. What is the sample space of this experiment S=[TTT, TTH, THT, THH, HTH, TTH, HHT, HHH] b. Find the probabilities that i. exactly two of the three tosses are heads. Let X=number of Heads. P(X=2)=3/8 ii. at least two tosses come up tails Let Z=number of Tails. P(Z>=2)= P(Z=2)+P(Z=3)=3/8 + 1/8 =1/2 iii. all three tosses come up the same P(Z=3 U X=3)= P(Z=3) +P(X=3) =1/8 + 1/8 iv. the second toss is heads. Let Y=1 if second toss is Heads (zero otherwise). P(Y=1)=4/8=1/2 2. Assume you are rolling an 8-sided die. Consider the following events: A=[even numbers], B=[prime number greater than 3], C=[1,2,3,4] a. Show that A U (B ∩ C) = (A U B) ∩ (A U C) (B ∩ C) = empty set and A=[2,4,6,8] thus A U (B ∩ C)=[2,4,6,8] (A U B) = [2,4,5,6,7,8] and (A U C) = [1,2,3,4,6,8] thus (A U B) ∩ (A U C) =
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Econ 210 Spring 2009 Problem Set 1 - Solutions - Econ 210...

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