Let X be the payoff for one ticket in the raffle. This variable has two possible outcomes, that the ticket is a winning ticket, in this case, you will win $460, or that the ticket has no price, then the profit will be $0.
To determine the probability of each outcome, you have to divide the number of favorable outcomes (nº of tickets that have/have not prize) by the total number of tickets of the raffle.
The raffle has 250 tickets
1 ticket has a $460 prize
249 tickets have no prize
The corresponding probabilities for both outcomes can be calculated as follows:
[tex]P(460)=\frac{1}{250}=0.004[/tex][tex]P(0)=\frac{249}{250}=0.996[/tex]
You can arrange the possible values of X and their corresponding probabilities P(X) as follows:
