I have a chance/probability question.

Question

You currently babysit a family for an hour each day and make $10 an hour. The family knows that you are trying to save money, and offers you the following deal. You can either be paid the $10, or you can pull two bills from a brown paper bag. In the bag there are two $1 bills, two $5 bills, and a $10 bill. For example, you might pull out a $1 bill followed by a $5 bill, and earn only $6. Or you might pull out the $10 bill followed by a $5 bill and earn $15. If you were given this option every day, what would be better for you to do in the long run? Is pulling two bills from the paper bag a great way to make money? Be sure to give a complete explanation of how you found your answer.

Answer 1

You need to compute expectation of this probability distribution:

 

P(X1=10,X2=5)=.2*.4=0.08,15$

P(X1=10,X2=1)=0.2*.4=0.08,11$

P(X1=5,X2=10)=0.4*.2=0.08,15$

P(X1=5,X2=5)=0.4*.4=.16,10$

P(X1=5,X2=1)=0.4*.4=.16,6$

P(X1=1,X2=10)=0.4*.2=0.08,11$

P(X1=1,X2=5)=0.4*.4=.16,6$

P(X1=1,X2=1)=0.4*.4=.16,2$

 

 

Hence expectation is equal to:

 

E(x)=15*.08+0.08*11+0.08*15+10*.16+.6*16+0.08*11+.16*6+.16*2=8$

 

Hence in long run, on average you are going to make 8$/day and this is a bad deal.