Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance x is exactly (1-x/q), where q is a real constant greater than 50.
During each practice run, she takes shots from distances x=1, x=2, ..., x=50 and, according to her records, she has precisely a 2% chance to score a total of exactly 20 points.
Find q and give your answer rounded to 10 decimal places.