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) =