You and your colleagues have randomly chosen 15 children from the city schools to pilot your new reading program starting this January. An irate parent (in an editorial to the local newspaper) claims you are favoring males in
your selection. Your random sample has 9 males and 6 females. (The entire population of children this age in your community, from which you have chosen your sample, is 70% male and 30% female.)
1.How likely is it to draw a sample of 15 with 6 or fewer females from this
population?

Question

You and your colleagues have randomly chosen 15 children from the city schools to pilot your new reading program starting this January. An irate parent (in an editorial to the local newspaper) claims you are favoring males in 
your selection. Your random sample has 9 males and 6 females. (The entire population of children this age in your community, from which you have chosen your sample, is 70% male and 30% female.)
1.How likely is it to draw a sample of 15 with 6 or fewer females from this 
population?

anonymous · Answer

What is the prob of choosing all males?

anonymous · Answer

If we assume the entire population is really big

lukecrayonz · Answer

The parents seem to not like it @Redcan

anonymous · Answer

At least one editorial writing parent.

anonymous · Answer

Ok, hint #2... Are the events that you choose no females and exactly one female independent?

lukecrayonz · Answer

I would assume so

anonymous · Answer

I agree, you can't choose exactly one and exactly 0 at the same time

anonymous · Answer

So now we know, $$P(k\le 6)=P(k=0)+P(k=1)+\dots+P(k=?)$$