Example: Florida lotto

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 12) 4/51
• P(match 4th given 123) 3/50
• P(match 5th given 1234) 2/49
• P(match 6th given 1234) 1/48

2
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 states k)

3
Probabilities for Lotto (Pick 6)

• EXCEL Function HYPGEOM.DIST(y,n,k,N,0) returns
  P(Yyn trials, k Ss in population of N items)
• HYPGEOM.DIST(y,n,k,N,1) returns P(Yyn trials,
  k Ss in population of N items)

Repeat this for Fantasy 5. You and state select 5
from 1 to 36