Question 144879
You have part a done correctly.  Steven (or anyone else for that matter) can expect to lose -$1.14 for every $2.00 spent.  In other words, the game is rigged (way, way, way) in favor of the house.


The fair price for a ticket is that price that would make the expected value be zero.  So, reuse your expected value formula, this time using a variable {{{P[f]}}} in place of the $2 in your previous calculation and set it equal to 0:


{{{400(1/1000) + 200(1/1000) + 50(5/1000) -(P[f]) (993/1000) = 0}}}


Solve for {{{P[f]}}} and you have your fair price.