Part 1 ยท Birthday Paradox
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Birthday paradox

Do any two people in this room share a birthday?

Not the year, just the day and month. Who thinks there is a match?

50.7%
23 people
70.6%
30 people
97%
50 people

Let's test it. Who was born in January? Say the day...

โ†“ reveal the odds โ†“ test it live

Part 1 ยท Birthday Paradox

Why so many?

We are not comparing "mine with everyone else's." We are comparing everyone with everyone.

Number of pairs = n(nโˆ’1)/2

  • 10 people โ†’ 45 pairs
  • 23 people โ†’ 253 pairs
  • 50 people โ†’ 1225 pairs

Not many people.
A huge number of pairs.
Each pair is a chance for a match.

Part 1 ยท Birthday Paradox

Exact calculation

It is easier to calculate the probability that all birthdays are different, then subtract from one.

P(all different) =
365/365 ร— 364/365 ร— 363/365 ร— โ€ฆ ร— (365 โˆ’ n + 1)/365
P(match) = 1 โˆ’ P(all different)

n = 23

1 โˆ’ 0.4927 = 50.7%

n = 50

1 โˆ’ 0.0296 = 97.0%

The first person has 365 free days. The second has 364. Each next person removes one more option, so the space shrinks faster than it feels.