How many people do you know? And how many of them share a birthday with you? The number is usually higher than you would expect. This is often seen in student classrooms where a group of 20 to 30 kids will have at least a couple of others sharing a birthday.
This is known as the birthday problem, or the birthday paradox, because you would think having 365 days in a year would require over 100 people to finally find someone with the same birthday. But with just 23 people, you already have better odds than flipping a coin.
We're afraid this is another problem, like the infamous Monty Hall one, that requires counter-intuitive probability.
Let’s start with just two people. The probability that you and another random person don’t share a birthday is very high 364/365 or 99.7 percent. If there are three people in the room, the probability that all have different birthdays is (364/365)x(363/365). That’s a probability of 99.2 percent.
The more people you add, the lower the percentage gets, but you don’t have to have 183 people to get to 50 percent. When you get to just 23 people, the formula above drops to a probability of 49.3 percent.
So the probability of sharing a birthday in a group the size of a classroom or work team is more than a flip of a coin. If you have 41 people, maybe the size of an office or department, your probability of sharing a birthday with someone else goes to over 90 percent. With 60 people it is over 99 percent. At 100 people, the chance that two of the group have the same birthday is 99.99997 percent.
So, if you don’t like sharing your birthday, small groups are best.