1. Example: Florida lotto
You select 6 distinct digits from 1 to 53 (no replacement)
State randomly draws 6 digits from 1 to 53
Probability you match all 6 digits:
First state draw: P(match 1st) = 6/53
Given you match 1st, you have 5 left and state has 52 left: P(match 2nd given matched 1st) = 5/52
Process continues: P(match 3rd given 1&2) = 4/51
P(match 4th given 1&2&3) = 3/50
P(match 5th given 1&2&3&4) = 2/49
P(match 6th given 1&2&3&4) = 1/48

2. Distribution of Winning Digits - Hypergeometric Distribution
N = Total # of digits in machine (53)
r = # of successes selected by state (6)
n = # of digits you select/sample (6)
Y = # of successes in your n selected (matches among your n and state’s r)

3. Probabilities for Lotto (Pick 6)
EXCEL Function: =HYPGEOM.DIST(y,n,k,N,0) returns P(Y=y|n trials, k Ss in population of N items)
=HYPGEOM.DIST(y,n,k,N,1) returns P(Y≤y|n trials, k Ss in population of N items)
Repeat this for Fantasy 5. You and state select 5 from 1 to 36

4. Numbers of Even and Odd Numbers
Results from 10/24/1999-8/29/2015: