In our simulation, 41 of the 100 rooms with 20 people have at least 2 persons that are born on the same day (41%). That's surprisingly high, right?
The
Birthday
Experiment
"How likely it is to have 2 or more people in the same room who have a birthday on the same day?"
Assumptions
Before we answer that question, we will make two assumptions here:
- 1. Any day of the year has the same probability to be a birthday;
- 2. We will consider that every year has 365 days.
The Experiment
If we use a little bit of frenquentist statistics theory,
we can assume that if we repeat an experiment a "lot" of times,
then the frequency of occurring some event is close to his probability.
(Thats sound a little boring, I know, but have faith!)
To be more clear, let's simulate 100 random rooms with 20 people each and then count how many "matches" do we have:
The Curve
If we simulate a lot of rooms with diferent sizes, then we get that curve:
With 23 people in the room, the probability of at least a match is about 50%!
With 42 people in the room, the probability increase to about 90%!
Hover over the curve to explore the simulations results:
The End.
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