Make sure you ask the question very clearly.

Q1. What is the minimum number of people you need in a room before it is more likely than not that two of them share a birthday?

The answer is 23. Bypass the next paragraph if you either are not interested in how the answer is calculated or already know the solution.

Without substantially altering the answer, we'll assume the year is 365 days long. We'll focus on the chance of everyone in the room having a different birthday.

• The first person enters the room. The second person has 364 out of 365 chances of having a different birthday to the first person.
  
• The third person has 363 out of 365 chances of having a different birthday to the other two.
  
• And so it goes on. The 23rd person has 343 chances of out of 365 of having a different birthday.
  
• Multiply all these probabilities together to get the probability of all the events happening. You can do it on your calculator.
  
• After 22 people have entered the room, the probability of them all having different birthdays is still greater than 0.5. But multiply that number by 343/365 when the 23rd person enters the room, and now the probability is less than 0.5, so it more likely than not that two of the people in the room share a birthday.
  

Q2. What is the minimum number of people you need in a room before it is more likely than not that one of them shares a birthday with you?

The answer is about 254. Each person who enters the room has 364 chances out of 365 of not having the same birthday as yours. If x is the number of people in the room needed, then we have to solve the equation (364/365)^(x-1) = 0.5.

What intrigues me is that the questions are very similar, yet the answers are very different: 23 versus 254. Indeed the questions are so similar that many people might not detect the nuance. If we put the questions through an automated translator (e.g. Babelfish), and translate them into, let's say, Spanish and back again, we get:

Q1. Whoever is the most minimum number of persons that you need in a quarter before you are more likely that no those two from her part in the birthday?

Q2. Whoever is the most minimum number of persons that you need in a quarter before you are more likely that no that one of the parts in the birthday with you?

Both sentences no longer make sense, although they still differ. Will anyone understand the questions? It's highly unlikely that anyone will come up with 23 and 254.

The moral of the story

I'm not trying to make a point about not giving numerical tasks to foreigners. The key issue is about clarification of the question. English can be a very compact language—small differences in wording yield very different answers. Mechanical translators have a long way to go before they can understand these nuances. (And I have to admit that it is mathematically interesting that the two answers are so different.)