[SGS]

Let X be your payoff from one play of the Lottery game. It costs $1.00 to play the game so if you lose then x = -1. To play Powerball you select 5 distinct numbers from 53 white numbers and 1 additional number from 42 red numbers. The state then randomly selects 5 distinct white numbers and 1 red number. For this problem we will assume that the Jackpot will pay $10,000,000.
The possible payouts are:
( a ) Match all 5 white and the red - pays $10,000,000
( b ) Match all 5 white only - pays $100,000
( c ) Match 4 white and the red - pays $5,000
( d ) Match 4 white only - pays $100
( e ) Match 3 white and the red - pays $100
( f ) Match 3 white only - pays $7
( g ) Match 2 white and the red - pays $7
( h ) Match 1 white and the red - pays $4

Note: When the Lottery claims you have won $4 actually you have won $3 since they do not return the dollar you paid to play. Remember this in your calculations.

Find the expected value of X.

I don't think I did this problem right, can anyone show me the correct way to go about this problem? Thanks in advance for any help.

SGS