Basketball Scores

A basketball player is taking 100 free throws. She scores one point if the ball passes through the hoop and zero points if she misses. She has scored on her first throw and missed on her second.

For each of the following throws, the probability of her scoring is the fraction of throws she has made so far. For example, if she has scored 23 points after the 40th throw, the probability that she will score on the 41st throw is $\frac{23}{40}$.

Question: After 100 throws (including the first and the second), what is the probability that she scores exactly 50 baskets?