An Answer Page for Exercise 4

Exercise 4

What would the lottery prize need to be for our expectation to be positive ?


From example 6,   we have   E   =   Zp - 1 + p.

So,   E > 0     Zp   >   1 - p     Z   >   ( 1 - p ) / p     Z   >   c - 1   =   13,983,815

The prize would have to be greater than   $13,983,815.

For prizes bigger than this amount the advantage would be in our favor if we could afford to play a large number of times ( see exercise 5 ). Most of us could never afford to do this, and it is unrealistic to expect such a big prize to be offered for the thousands of trials it might take us to achieve our first win.