I enjoyed reading your thoughts on luck. I think you need to focus on the question a bit more-- it asks "Are you a lucky person? Do you believe in luck?" So, you should answer this question-- yes or no. Then explain why. I see where you have written> So what is luck and how can we measure it? I think this notion should not be so close to the ending of your paper. Also, remember to answer the question by saying more about how you are or are not lucky. Also, you could do a brief comparison of luck and success. Luck is very different. For example, a man who fishes for the first time, and catches a fish, is lucky, because he does not have any practice (this is the same kind of luck that the old woman in your story has) Success, on the other hand, is a man who practices fishing and has great skill, then catches a fish, he has success. I think you should speak from your point of view, in order to best answer the question, instead of saying "research has shown..." etc.
Your passage is very interesting. It stimulates my thoughts and I really like it!
By the way, I agree with Jennyflower81 that you should answer the first question in the first paragraph. It would make the whole picture clearer.