Question 1194556
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At a raffle, 2000 tickets are sold at $3 each for four prizes of $600, $250, $200, and $80. You buy one tickets.
A) What is the expected value of your gain?
B) interpret the results.
C) is this a fair game? Explain.
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<pre>
Bying one ticket, you have 

    - the probability of  {{{1/2000}}}  to win $600,  or

    - the probability of  {{{1/2000}}}  to win $250,  or

    - the probability of  {{{1/2000}}}  to win $200,  or

    - the probability of  {{{1/2000}}}  to win  $80.


The expected value is then  E = {{{600/2000 + 250/2000 + 200/600 + 80/2000}}} = {{{(600+250+200+80)/2000}}} = {{{1130/2000}}} = 0.565  dollars.


Paying #3 for each ticket, the expected value of the game is  $0.565 - $3 = -$2.435.


In other words, playing many times, the gamer loses $2.435 in any game, in average.


The game is unfair.
</pre>

Solved and explained.