A raffle offers a first prize of 1000 2 second prizes of 300

A raffle offers a first prize of $1000, 2 second prizes of $300 and 20 third prizes of $10 each. If 8000 tickets are sold at 75¢ each, find the expected winnings (IN CENTS) for a person buying 1 ticket.

Solution

75 cents mean $0.75. Let X shows the wining amount by the person. Since person buy only 1 ticket so X can take values $1000-$0.75=$999.25 or $300-$0.75=$299.25 or $10-$0.75=$9.25 or -$0.75 (if person does not win). Since there is only first proze so

P(X=$999.25)= 1/8000

There are 2 second prize so

P(X=$299.25)= 2/8000

There are 20 third prize so

P(X=$9.25)= 20/8000

And rest 8000-(1+2+20)=7977 do not have any prize so

P(X=-$0.75)= 7977/ 8000

So the expected winnings for a person buying 1 ticket will be

E(X)= $999.25*(1/8000)+ $299.25 *(2/8000) + $9.25* (20/8000) + (-$0.75) * (7977/8000)=$0.22275

So  the expected winnings (IN CENTS) for a person buying 1 ticket is approximately 22 cents.