Mean probability of lotto integer?

Can somebody please tell me where or how I might find a formula
for calculating the mean probability for an integer in a lotto n/N
type game. In this game one must select n integers out of N.

The winning combination of integers is determined by drawing
one ball or integer at a time without replacement.

Thus on the first draw the chance of drawing a specific
integer must be 1/55, on the 2nd it is 1/54, on the 3rd it is
1/53, on the 4th it is 1/52 and onthe 5th it is 1/51.

The sum of these fractions is =0.094407=5/53=1/10.6=5.2/55.
An alternative formula implies the value should be
1- (54/55)^5=0.87663=1/11.4=4.8/55. With replacement it would
be 5/55=1/11.

Is any of these formula correct, and if not, what type of formula
should be used? The second seems more realistic.

Is there a textbook dealing specifically with this problem?

Once the probability has been established it should be possible
to determine the std.dev. for the mean frequency of integers after
hundreds and thousands of draws to test if the draws were bbiased.
Other tests have been used, such as the chi-squared test. In an actual
test of 17511 runs of the 6/49 game from world wide records the s.d
was 55.44 while above formulas would suggest a value around 43.

Stig Holmquist



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