SOLUTION: Lottery Prizes A lottery offers one $900 prize, two $700 prizes, two $400 prizes, and five $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person b

Question 1209575: Lottery Prizes A lottery offers one $900 prize, two $700 prizes, two $400 prizes, and five $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys three tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I don't know what to make of the statement that "the player's ticket is replaced after each draw and that the same ticket can win more than one prize". That seems unusual; and I'm not sure it changes how to calculate the expected value.

I will leave it to another tutor to show a solution using the formal definition of expected value. A less formal common sense solution is much easier.

The total cost of the tickets is 1000*($5) = $5000.

The total payout is $900 + 2*($700) + 2*($400) + 5*($100) = $3600.

Overall, the "gain" is $3600 - $5000 = -$1400.

The expected value for each of the 1000 tickets is (-$1400)/1000 = -$1.40.

The expected value for 3 tickets is 3*(-$1.40) = -$4.20.

ANSWER: -$4.20

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
Lottery Prizes A lottery offers one $900 prize, two $700 prizes, two $400 prizes, and five $100 prizes.
One thousand tickets are sold at $5 each. Find the expectation if a person buys three tickets.
Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize.
Round to two decimal places for currency problems.
~~~~~~~~~~~~~~~~~~~~~~~~~~

The hidden meaning of this problem is that, although the tickets are replaced, the prizes are not replaced.

In this formulation, each next round is different from the previous.

Unfortunately, this Math composer does not have enough mathematical culture
to communicate with his readers in a right mode.

Besides of it, it is unclear, for which reason three tickets are bought, if the tickets are replaced.

Also, it is unclear WHEN the game stops.

So, there are too many uncertainties to consider this post as a sensical Math problem.

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