Question 1197615: A certain raffle has one ticket that wins a $150 prize and five tickets that each win a $10 prize out of 150 purchased tickets.
Round answers to the nearest cent.
a. Find the expected value of each ticket.
b. For the company running the raffle, would selling each ticket for $5 be a Profit, a Loss, or a Fair Game?
Answer by math_tutor2020(3817)   (Show Source):
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Part (a)
Answer: $1.33
Work Shown:
X = winnings
| X | P(X) | X*P(X) | | 150 | 1/150 | 1 | | 10 | 5/150 | 1/3 | | 0 | 144/150 | 0 |
Add up the results in the X*P(X) column
E[X] = 1+1/3+0 = 4/3 = 1.33 approximately
The expected winnings is $1.33 approximately.
The player expects to win on average $1.33 per ticket (this is before the cost of the ticket is factored in).
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Part (b)
Answer: Profit
Reason:
The company expects to lose $1.33 per game when paying out the average winnings per ticket, as we found in part (a).
However, they gain $5 per ticket if they go for this ticket price.
The net profit per ticket from the company's perspective is -1.33+5 = 3.67
The company expects to gain $3.67 per ticket; while player expects to lose $3.67 per ticket.
These values represent averages.
If the ticket price was $1.33, then both sides neither win nor lose money. In such an event, we consider it a fair game.
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