SOLUTION: a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. one thousand tickets are sold at $3 each. find the expectation if a person buys one ticket.
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-> SOLUTION: a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. one thousand tickets are sold at $3 each. find the expectation if a person buys one ticket.
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Question 1197971: a lottery offers one $1000 prize, one $500 prize, and five $100 prizes. one thousand tickets are sold at $3 each. find the expectation if a person buys one ticket. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 1 ticket is sold at a cost of 3 dollars.
the probability of getting 1000 dollars back is 1/1000.
the probability of getting 500 dollars back is 1/1000.
the probability of getting 100 dollars back is 5/100.
the expectation on one ticket is therefore -3 * 1/1 + 1000 * 1/1000 + 500 * 1/1000 + 100 * 5/1000 = -1.
the person's expectation is to lose an average of one dollar per ticket.
one way to look at it is:
if the person buys all the tickets, the cost to the person is 3000 dollars.
the prize money the person will receive is 2000.
divide that by 1000 tickets sold to get an average loss of 1 dollar per ticket.
