Have you ever been sung to at a restaurant on your birthday? Usually this is for kids but it would be interesting to see how old a person has to be before it gets creepy to insist that the staff sing to you, leave a comment if you conduct this field research. 

Here's the problem: 

The problem is relevant to you since you care about singing as least as possible; something everyone (except Shakira and drunk people doing karaoke of Shakira) should strive to do. Mathematically speaking the problem has a simple counting solution but leads to a counter-intuitive solution so you might see it (or a variation of) talked about often on Reddit and  this variation was even covered by Khan. 

Consider the birthday boy/girl to be sung at, suppose their birthday falls on some date D. Imagine asking the other guests one at a time what their birthday is. The first guest has a 364/365 chance of not hitting the hosts’ birthday when asked as there are 364 other days that it could be. The second guest chimes in but also has a 364/365 chance of not hitting the right date D as we don’t care if guest 2 matches with guest 1, only that he/she match with the birthday boy/girl. Similarly each consecutive guest will have this same 364/365 chance of hitting that particular birthday. As each birthday is an independent event (if they weren't their parents would have some explaining to do) we can multiply their odds to get an inclusive probability of no-one else having the birthday D. Suppose there are "n" (other than the bday boy/girl) guests in the party, then the converse of the event E that there is no guest with the birthday of D is: 

We can use the encompassing property of probability to get the event probability itself: 

The question, for you the waiter doing this in your head, is what should "n" be in the above probability so that it is greater than fifty percent? You cower back to the kitchen entrance and scribble the following out on a napkin (algebra students, please check my work): 

Note that this variation is different than the traditional one in the sense that we fixed the birthday D ahead of time! The traditional problem dictates only that two people share any birthday which obviously opens up more possibilities. To illustrate this, I have graphed the traditional problem in blue against our problem in red. The MATLAB code to generate this is here.