The Birthday Problem

The Birthday Problem asks: how many people need to be in a room before there's a better-than-even chance that at least two share the same birthday? Surprisingly, this number is only 23. This occurs because each new person added creates multiple potential birthday matches with everyone already present. The probability that all birthdays are unique decreases rapidly as more people join. When you reach 23 people, the chance of at least one shared birthday surpasses 50%. This counterintuitive result highlights how probability accumulates quickly in groups, making shared birthdays more common than intuition might suggest.