So the birthday paradox is where if you’re in a room with 23 other people there’s a 50% chance of at least two people having the same birthday. Alternatively, In a room of 75 there’s a 99.9% chance of at least two people matching.
Why is this?
In: 134
The odds are so high because you’re not checking to see if *you* have the same birthday as some else in the room. Instead you’re checking to see if person A has the same birthday as person B, or C, or D, etc…and then *also* seeing if person B has the same birthday as person C, or D, or E, etc…and then *also* seeing if person C has the same birthday as person D, or E, or F, etc…and then *also* seeing if person D has the same birthday as person E, or F, or…
As you see, the number of combinations that you’re checking explodes *much* more quickly than you might first thing. As it turns out, with only 23 people you end up checking *so many combinations* that it’s actually a good bet that at least one of them will be a match.
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