100 raffle tickets are sold for 3 dollars each. One prize of 200 is to be rewarded. Raul purchased 1 ticket.
what is his expected value and what his his fair prize
To determine Raul's expected value and fair prize, we need to calculate the probability of him winning and losing, and then multiply them by their respective outcomes.
1. Probability of winning:
Raul purchased 1 ticket out of 100, so the probability of him winning is 1/100.
2. Probability of losing:
Since there is only one prize, the remaining 99 tickets will not win, so the probability of losing is 99/100.
3. Winning outcome:
If Raul wins, he will receive a prize of 200 dollars.
4. Losing outcome:
If Raul loses, he will not receive any prize, resulting in a value of 0 dollars.
Now we can calculate the expected value and fair prize.
Expected value:
The expected value is calculated by multiplying each outcome by their respective probabilities and summing them up.
Expected value = (Probability of winning * Winning outcome) + (Probability of losing * Losing outcome)
Expected value = (1/100 * 200) + (99/100 * 0)
Expected value = 2 dollars
Therefore, Raul's expected value is 2 dollars.
Fair prize:
The fair prize is the amount of money that Raul should expect to pay for the ticket in order to make it a fair game. In other words, it is the expected value divided by the probability of winning.
Fair prize = Expected value / Probability of winning
Fair prize = 2 dollars / (1/100)
Fair prize = 200 dollars
Therefore, Raul's fair prize is 200 dollars.