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

Distribution of Winning Digits - Hypergeometric Distribution N = Total # of digits in machine (53) k = # 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 k)

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