Ann has a choice of two babysitting payment options:

1. She can accept a flat rate of $15 for a night's work, or:
2. She can choose two of six sealed envelopes containing $1, $1, $5, $5, $10 and a $20 bill.

(For example, the second option could leave Ann with as little as $2 or as much as $30 for a night's work.)

Assuming that Ann will have to babysit for a very long period of time, which is the better payment option for her?

choice 1 has an expected payment of $15.

For choice two there 8 are ways to draw two envelopes which are listed below along with their corresponding probability:
(1,1) (2/6)*(1/5)=2/30
(1,5) 2*(2/6)*(2/5)=8/30
(1,10) 2*(2/30)=4/30
(1,20) 2*(2/30)=4/30
(5,5) 2*(2/30)=4/30
(5,10) 2*(2/30)=4/30
(5,20) 2*(2/30)=4/30
(10,20) 2*(1/30) = 2/30
so the expected payment comes out to:
(2/30)*(2+30)+(8/30)*6+(4/30)*(11+21+10+15+25)=
440/30=44/3=14.666666

So the flat rate of $15 is the better option.

Posted by Daniel on 2013-08-13 10:27:59