What type of probability distribution is this ? that's the first question.
Given that there are no restrictions mentioned,
conceivably a class could contain all girls or all boys.
The probabilities of a class containing (i) 0 girls and 25 boys, (ii) 1 girl and 24 boys, (iii) 2 girls and 23 boys,
(iv) 3 girls and 22 boys ..... up to 25 girls and 0 boys
covers the spectrum and so those probabilities sum to 1 here.
The Binomial distribution can handle this.
All the terms of the binomial expansion of (g+b)[sup:500e0he0]n[/sup:500e0he0] correspond to those probabilities,
where g is the probability that a student is a girl and b is the probability the student is a boy.
n is the number of students in a class.
Calculate g and b from the total number of girls and the total number of boys.
Check how the Binomial is expanded out and try to decipher how to calculate the probability
of having 15 girls and 10 boys in the class,
as this question is asking you for the probability of exactly 15 girls in the class,
not "at least" or "at most".
Same story for question (b).
For (c) you need the probabilities of the class having 21 or 22 or 23 or 24 or 25 girls.
Then you need to think of the fact that there are 4 classes.
