if you sell 1000 1 raffle tickets and the only prize is 500t

if you sell 1000 $1 raffle tickets and the only prize is $500,there is a mathematical expectation of what for a single ticket?

Solution

for the total 1000 tickets, there is only 1 prize.

p=1/1000

Here x value is 500-1 because you spend $1 for buying the ticket. hence x=499

the remaining 999 tickets do not have any prze.

p=999/1000

here there are no gains, only spending $1 for buying hte ticket. hence x=-1

E(x)=sum(x*p)=sum(499*1/1000-999/1000)=-500/1000=-0.5