The chances actually are moderately low that they won’t.
You only need a group of 20 people to have more than a 50/50 chance that two have the same birthday, and at 40 or so in the group it is highly probable that two will have the same birthday.
To set a specific date obviously sets limits, but it is quite possible that two people on here out of 1,000 have a birthday on 30 August.