Statistics

The registration numbers of vehicles in a certain country use digits 1-999. If a visitor has just entered the country. What is the probability that the first car he sees has at least 2 identical digits?

Ans: 29/111

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asked by Ariana
  1. Assuming leading zeroes count as digits, then probability of seeing 3 distinct digits
    = 10*9*8/1000
    = 720/1000
    =18/25
    Probability of at least 2 identical digits
    = 280/1000
    =7/25

    If leading zeroes are not displayed, then
    there are 9*9*8=648 plates with distinct digits between 100-999
    and 90 between 1 and 99
    for a total of 738 out of 999 plates.
    So probability of plates with at least 2 identical digits is
    (999-738)/999
    =29/11

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    posted by MathMate
  2. Last line should read
    29/111

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    posted by MathMate
  3. How do you get 738/999??

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    posted by Ariana

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