Hard probability question...

When you leave the movie theater, an usher tells you that there were 175 girls and only 25 boys in the theatre.

A) This makes you wonder who was sitting in the row behind you (rows have 10 seats). Find the probability that the row behind was all girls, 9 girls exactly, 8 girls exactly 7 girls exactly, 6 girls exactly, and at least 6 girls.

So guys can you show me how to do 10 girls exactly and at least 6 girls. I can figure out the rest if i see how exactly this is solved.

Did you quote this question verbatim?  Because if you did, then you don't need to do any math, and I'll tell you why.

The set-up does not mention the number or rows or whether the theater was either partially (in terms of percentage) or completely filled.  I know it says that there are 10 seats per row, and so one would assume that there are 20 rows, but that is not necessarily true.

Answer with a simple "Not enough information" and explain why.

>>2
If you want 0 marks maybe. Give that answer and then give the answer they obviously want, assuming that all rows are filled.

For exactly 10 girls, it would be (175 choose 10)/ (200 choose 10), or (175C10)/(200C10) if you prefer. This would be not counting yourself, though. If you are given whether you are a boy or a girl, subtract 1 from 200 and possibly 1 from 175 (Since you know where you sat, you shouldn't be included in the probabilities).

For at least 6 girls, you would add the probabilities of exactly 10, 9, 8, 7, and 6 girls together. Basically add together everything you've solved for so far.

Just get them to climb over the seats and fuck the boys.  They'll only go for the biggest, loudest asshole in the theater, so 1.

I had this same problem for math. you forgot to mention there are 10 seats in a row. so it would be (10nCr10)(7/8)^10 (1/8)^0 for all girls and (10nCr9)(7/8)^9 (1/8)^1  for 9 girls and one boy and so on and so forth.  for at least 6, its like the third person stated, you add all of those probabilities up

>>6
While 175/200 does equal 7/8, you seem to be forgetting that once a girl has taken a seat, they can't take another seat in the same row. Thus the entire (7/8)^10 makes no logical sense. It would have to be (175/200)*(174/199)*... or simply (175 nCr 10).

Also I'm not sure I understand why you choose the 9 seats first and then chose 9 girls and 1 boy. In fact, doing it this way yields an absurd probability.

>>6
Ok nevermind I do see why you chose to do the (10 nCr 9) part. It allows us to count all of the different ways that the one boy can sit amongst the 10 girls.

However, this is useful for counting the number of ways that this arrangement can be done. But for probabilities, this needs to be reconciled with the entire sample space, which right now I only see as (200 nCr 10), and I think that order like this goes away. Otherwise, it does give a quite absurd probability of 300 something percent.

I've got your hard probability right here.

lol u

Of course it's going to be assuming a number of things, but do not lawyerball math questions. It's the easiest way to piss off a teacher. you need to be able to determine the probablity of all girls, so, naturally you'll need to use the rule of multiplication.

All you do is find P(X) where x= 10 girls exactly.

So, you find the probability that the person at the end is a girl. That's 25/175 or 1/8. The chance of two girls being stationed together (statistically) is going to be 1/8*1/8 or 1/8^X where x is the # of girls in that row.

So, go ahead and just write the above and plug in the constant required.

Also: RTFM

oh fuck he's right

>>10
What are you talking about? For starters, there are 175 girls, not 25.

Secondly, yes, the probability that the person at the end of a row is a girl, without anything else known, is 175/200, or 7/8. That part is correct. But the probability that two girls sit next together is not (7/8)^2. That's absurd. That's saying that the same girl can sit next to herself.

It should be (175/200)(174/199), or (175 nCr 2). This has been said before. We are "drawing" girls without replacement, the without replacement being your mistake.

>>12

Oh Jesus Fuck you're right!

By god!

*smokes corncob pipe*

>>1
1. Why in the world did the usher have this information or feel it necessary to present it to you?
2. Did you not see/hear/notice who was behind you during the movie?
3. How many seats are there in the theater? There could be empty seats.
4. Was the information the usher presented including yourself? If so, what gender are you. If not, then there are either 201 seats in the theater made of rows of ten or empty seats.

You could use the binomial distribution, maybe
n,p,x
pdf
n=10
p=175/200
x=(10,9,8,7,6)
1-bicdf(10,175/200,5)
for pdf (.26308,.37582,.2416,.09204,.02391)
for cdf .99555
dunno if this is correct reasoning on my part

>>who was sitting in the row behind you

I was.

Not a single comment on the verbage of "How to do 10 girls"... I am so fucking ashamed of you nerds.

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