What are the chances of meeting a person born on the same day as you are, assuming that you were born in a non-leap year? One in 365?
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Person A can be born on any day of the year since they’re the first person we’re asking. The probability of being born any day of the year is 1 or more specifically: 365/365.
Since Person B must be born on the same day as Person A their probability is 1/365.
We want both of these events to happen so multiply the probabilities:
1 *1/365=1/365
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