Please show all work in an organized fashion for full credit.

Instructions: Please show all work in an organized fashion for full credit.

Problem 1.FindC1[C2andC1\C2if

(a)C1=f0;1;2g,C2=f2;3;4g;

(b)C1=fx: 0< x <2g,C2=fx: 1x <3g.

Problem 2.Suppose our sample space isf(x; y) :x2+y21g. What is the complementof the set/eventA=f(x; y) :x2+y2= 1g?

Problem 3.To join a certain club, a person must be either an economist, or a statistician,

or both. Of the total members in this club, 76% are economists, and 64% are statisticians.

What percentage of persons in the club are both an economist and a statistician?

Problem 4.After a hard-fought football game, it was reported that, of the 11 starting

players, 8 hurt a hip, 6 hurt an arm, 5 hurt a knee, 3 hurt both a hip and an arm, 2 hurt

both a hip and a knee, 1 hurt both an arm and a knee, and no one hurt all three. Comment

on the accuracy of the report.