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Mile of Pi - Numberphile

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The team from Numberphile printed one million decimal places of Pi onto a piece of paper which stretched for over a mile. They rolled it out on a runway usually used for testing planes and cars.

What is the probability that your birthday DD/MM/YY is found within the first million digits of Pi? How does that probability change if your birthday is represented using DD/MM/YYYY (four digits for the year)?

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