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THE BIRTHDAY PROBLEM

THE BIRTHDAY PROBLEM. Ivana Vuksanović. How many people do you need in a group to ensure at least a 50 % probability that 2 people in the group share a birthday? . 23. Proof:. one person - 365 distinct birthdays

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THE BIRTHDAY PROBLEM

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  1. THE BIRTHDAY PROBLEM Ivana Vuksanović

  2. How many people do you need in a group to ensure at least a 50 % probability that 2 people in the group share a birthday?

  3. 23

  4. Proof: • one person - 365 distinct birthdays • two people - 364 different ways that the second could have a birthday without matching the first • three people -363 different birthdays that do not match the other two => the probability of a match : 1 - (365)(364)(363)/(365)(365)(365)=0.82% . . . . . . • N people: the probability of a match 1 - (365)(364)(363)...(365 - N + 1)/(365)^N -for N=23 => the probability of a match is 50,73%. Q.E.D.

  5. random birthday applet

  6. N- number required to have a probabilitygreater than 50%K– matches

  7. Formula for the probability of a match: 1-(364/365)^(n-1) • N=23 – probability : 6,1% • N=253- probability: 49,91% • N =254 – probability: 50,05%

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