Okay, I'm really bad at probabilities but I will try it...
I will use the question I said just because it's easier.
Also, I think I should have said that each time you take one person out of the room, a new person comes into the room.
If you don't replace the person you took out, then it changes the answer.
SO
Probability of first person to have on a blue shirt: 85/100
Probability of second person to have on a blue shirt: 85/100
Probability of third person to have on a blue shirt: 85/100
...and so on...
Multiply all the probabilities together:
\(\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100} \\~\\ =(\frac{85}{100})^9 \\~\\ \approx 0.2316\)
So about a 23.16 % chance.
I know this is probably the worst way of doing it but I tried...