Question 1165788
. 
The current Powerball jackpot is estimated to be $193 million. 
The Powerball lottery is decided every Wednesday and Saturday night by drawing five white balls 
out of a drum with 69 balls and one red ball out of a drum with 26 red balls. 
The Powerball jackpot is won by matching all five white balls in any order and the red Powerball. 
Each ticket costs $2. What is the expected value for purchasing one ticket for the jackpot?
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<pre>
The total number of all possible quintuples of integer numbers from 1 to 69, with no repeating, is

    {{{C[69]^5}}} = {{{(69*68*67*66*65)/(1*2*3*4*5)}}} = 8259888

(the number of combinations).


So, the probability to get the winning ticket is

    P = {{{1/(8259888*26)}}}.


Thus the expected value of this lottery for purchasing one ticket is

    {{{193000000/(8259888*26)-2}}} = -1.101310221  dollars.
</pre>

Solved.