Should you ask her out?

Let’s say that you are feeling like going out tonight. You feel great and decide to go out for a drink with your friends. At the bar, you spot a (randomly selected) cute girl. You decide to start a conversation and, since she seems to be really nice, you wonder if she would accept to go on a date with you. After a couple of hours (and perhaps some drinks), you get the courage to ask her out. Unfortunately, she tells you she has a boyfriend. Discouraged, you return to the table where your friends are and explain the situation. After listening to you, your friends tell you that you should insist. After all, some girls just play hard to get. You struggle to decide what you should do about it. However, you are confident that your knowledge of probability should help you solve this dilemma.