First the hard facts:
In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching.
Sounds crazy? Well at the first glance, but simple statistics and the assumption that birthdays are distributed equally across the year (ignoring leap years) can explain this fact. For those who are interested in how these number can be derived I recommend the quite good explanation at Wikipedia. The really hard to grasp fact (although again simple math) comes when you ask yourself how many people need to be in a room to have a 50% chance that one person has the same birthday as you? This number equals to be at least 253. This is significantly higher than 365/2 = 182.5. An explanation for this can be found on the same Wikipedia page. Thus, although Japanese train cars are really crowded during commuting hours chances that someone is having the same birthday as me are not much above 50%