In a function girls were allowed to wear only red, blue or black dress. If 15 girls were wearing red, 10 girls were wearing blue and 20 girls were wearing black, then the probability that a girl selected at random was not wearing black dress is: 

$\frac{5}{9}$

According to the question,

15 girls were wearing red, 10 girls were wearing blue and 20 girls were wearing black.

Girl not wearing black = 15 + 10 = 25

Total girls = 45

So, the probability of that a girl selected at random was not wearing black dress is = \(\frac{25}{45}\) = \(\frac{5}{9}\)