Computer Simulation

If you go one of the leland computers and call the program matlab you will be able to try the following example:

rnum=floor(100*rand(1,50)+1)

ans=
  Columns 1 through 12 
 76    16    72    85    79   100    59    37    38    99    89    19
  Columns 13 through 24 
 25    25    18    34    41    63    90    68    14    48    97    50
  Columns 25 through 36 
 40    99    77    99    24    47     4    74    85    52    15    78
  Columns 37 through 48 
 45    17    26    73     7    12    82    47    91    90    21    88
  Columns 49 through 50 
 24    69


sum(rnum<51)
 
ans =
    25

This means that out of the 50 simulated numbers there were 25 that were strictly smaller than 25. Nearly too good to be true!

Try it, you will get a different set of numbers, but should get similar results.

This is the basic motivation of why probability is so related to combinatorics (ie enumerating or counting the cardinal of sets).