Question 1092168
<br>Of course, the usual way to calculate the expected profit for one ticket is to multiply the probabilities of each outcome (kind of prize) by the value of the outcome (the prize value), add all those results, and subtract the cost of your ticket.<br>
1 grand prize of $2000: {{{(1/800)*2000}}}
3 second prizes of $300 each: {{{(3/800)*300}}}
15 third prizes of $20 each: {{{15/800)*20}}}<br>
We don't need to calculate the expected return on the other 781 tickets, since each of them has a return of $0.<br>
The total expected return is then<br>
{{{(1*2000+3*300+15*20)/800 = 4}}}<br>
So the expected return on each ticket is $4; since the cost of the ticket is $5, your expected profit is -$1.<br>
But for this kind of expected value problem, there is a much easier way to find your expected value for a single ticket.<br>
The council is selling 800 tickets for $5 each, so their income is $4000.  They are giving out prizes worth a total of $3200, so their profit is $800.  That means their expected profit (per ticket) is $1... and that means your expected profit for one ticket is -$1.