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The birthday problem concept question

  1. Jun 5, 2014 #1
    Let A(i) be the event that the first ith person have different birthdays for i=1,2,3...,n.
    We note that A(i+1) is a subset of Ai such that Ai(A(i+1))= A(i+1)

    I wonder why A(i+1) is a subset of Ai. If the first 3 people have no birthdays in common, shouldn't that also mean the first 2 people doesn't either? By that logic, shouldnt Ai be the subset of A(i+1)?
     
    Last edited: Jun 5, 2014
  2. jcsd
  3. Jun 6, 2014 #2

    mathman

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    Your reasoning is correct up to the conclusion. Ai includes i+1 people who have same birthday as one of the first i, as well as all of A(i+1), therefore Ai is the bigger set.
     
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