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Example: Florida lotto

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 1 st ) = 6/53

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Example: Florida lotto

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  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:

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