Question 1191726
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Connecticut Lottery In the Cash Five Lottery in Connecticut, a player pays 1 dollar 
for a single ticket with five numbers. Five balls numbered 1 through 35 are randomly 
chosen from a bin without replacement. If all five numbers on a player's ticket match 
the five chosen, the player wins 100,000 dollars. The probability of this occurring 
is 1/(324,632) If four numbers match, the player wins 300 dollars 
This occurs with probability 1/2164 If three numbers match, the player wins 10 dollars 
This occurs with probability 1/75 . 
Compute and interpret the expected value of the game from the player's point of view.
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            Actually,  the probabilities to match four numbers or three numbers are  DIFFERENT 

            from that shown in the problem's formulation.



<pre>
The probability to match &nbsp;4 &nbsp;(four) &nbsp;numbers &nbsp;(if the order does not matter) &nbsp;is 

     P(4) = {{{C[35]^4}}} = {{{(35*34*33*32)/(1*2*3*4)}}} = {{{1/52360}}};


The probability to match &nbsp;3 &nbsp;(three) &nbsp;numbers &nbsp;(if the order does not matter) &nbsp;is 

     P(3) = {{{C[35]^3}}} = {{{(35*34*33)/(1*2*3)}}} = {{{1/6545}}}.


The probability to match &nbsp;5 &nbsp;numbers is as shown in the post.
</pre>

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So, &nbsp;the problem's formulation is &nbsp;EITHER &nbsp;incorrect &nbsp;OR &nbsp;should be explained in more details.



With the given data, the game expectation is


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;E = {{{100000/324632}}} + {{{300/2164}}} + {{{10/75}}} - {{{1}}} = -0.42.



It means that a player loses 42 cents in each game's ticket, &nbsp;in average.


It is so &nbsp;UNFAIRE &nbsp;game expectation &nbsp;that no one state regulator will allow such lottery.