Final answer:
The expected value of buying a raffle ticket in this scenario is approximately -$16.27, which means on average, a person expects to lose $16.27 per ticket purchased.
Step-by-step explanation:
To find the expected value for someone who buys a raffle ticket, we need to calculate the mean of the distribution of possible outcomes for a ticket purchase. In this scenario, a ticket costs $18, and the total number of tickets sold is 823. The winner receives $1400 plus the cost of their ticket, which is $18, so the total prize is $1418. The probability of winning the prize is 1/823, as there is only one winner.
The probability of not winning is 822/823. Therefore, the expected value (E) for a ticket can be calculated using the formula:
E = (Probability of winning × Winnings) + (Probability of not winning × Loss)
The loss is the cost of the ticket ($18) since you do not receive any prize if you do not win. So the calculation is:
E = (1/823) × $1418 + (822/823) × (-$18)
Now, we perform the multiplication:
- (1/823) × $1418 = $1.72 approximately
- (822/823) × (-$18) = -$17.99 approximately
Adding these together gives us the expected value:
E = $1.72 - $17.99
= -$16.2
Therefore, the expected value for a person buying a ticket is approximately -$16.27, which means on average, a person expects to lose $16.27 per ticket purchased.