In a states Pick 3 lottery game you pay 142 to select a sequ

In a state\'s Pick 3 lottery game, you pay $1.42 to select a sequence of three digits (from 0 to 9), such as 922.

If you select the same sequence of three digits that aredrawn, you win and collect $359.42

Find the expected value.

Solution

There are 9^3 = 729 wasy to choose a sequence.

Thus, the probability of winning is 1/729, and losing 728/729.

Now, consider the table:

x   P(x)   x P(x)
-1.42   0.998628258   -1.418052126
358   0.001371742   0.491083676
      
Sum(x P(x)) = -0.92696845
  
      
Thus,      
      
E(x) =    $ -0.92696845   [ANSWER]