Question

Earlier, someone asked a question of the form,
Given A girls and B boys
what is the probability of selecting X girls and Y boys?

For example, there are 3 girls and 3 boys. What is the probability of randomly selecting 2 boys and 2 girls (without replacement)?

I am curious as to what formulas for probability I am missing here.

Answer 1

use combinations
\[\rightarrow \frac{(3C2)(3C2)}{(6C4)}\]

Answer 2

Yes, but why those answers?

Answer 3

The denominator is consistent to http://en.wikipedia.org/wiki/Vandermonde's_identity

Answer 4

yes

Answer 5

and the numerator is is just common sense.

Answer 6

(by formulas I mean something like formula for event A and B, disjoint A and B, etc. Or even just something like binomial prob)

Answer 7

TIL that I have no common sense D:

Answer 8

at first.. we have to select x+y from a+b
this can be done by a+bCx+y ways
and to fulfill the condition, we have aCx * bCy ways
so, probability: \[^{a} C _{x} * ^{b} C _{y }/^{a+b}C _{x+y}\]

Answer 9

Oh no she didnt!

Answer 10

i cant guess any other method..

Answer 11

probability = desired outcomes/ total outcomes

6C4 is total ways you can pick 4 out of 6
picking 2 boys out of 3 AND picking 2 girls out of 3
2 independent events so multiply those outcomes

Answer 12

Actually, I think I understand it after Arnab explained it. Thanks everyone!

Answer 13

I am sure there must be another one using one of the convoluted probability distribution but this is the easiest in my opinion.

Answer 14

Arnab is good teacher

Answer 15

teacher? me!! OMG..

Answer 16

btw, how do you solve round table problems? Like, there are 5 people sitting at a round table... What do I divide 5P/Cr by?

Answer 17

Circular permutation.

Answer 18

n linear arrangement consists of 1 circular arrangement. So, when you have n people sitting round a table then you have n!/n =(n-1)! circular permutation. Note the clockwise and anticlockwise are considered distinct here. other wise you need to multiply by 1/2

Answer 19

Ah, thanks again :)

Answer 20

welcome. what does the username inkyvoyd signify?

Answer 21

It signifies the inability to come up with a creative username/ign, so I just picked two random works and misspelled one so it would be less likely to be taken.

Answer 22

lol, fair enough.

Answer 23

Btw, one last question (I came up with this after I took thought about the probability of taking guesses and getting a score on an actual test)

Let's say I have 60 multiple choice questions each with 4 choices and that the total score is 100(%).

Now, 20 of those questions are 3 points each, and 40 are 1 point each. Let's say that answer distribution is equal among the four choices (A,B,C,D). How would I find the probability of getting a score n?

Answer 24

are you in high school?

Answer 25

Freshman year. I self studied trig, precalc concepts, and calc one (not very well). I'm trying to learn calc 2, but it's going at a snail's pace. I've never taken a formal statistics course pre or post calculus, but I learned a little about normal distribution in an algebra 2 class.

Answer 26

That's great, this is actually a nice problem. Which I need to cogitate a bit.

Answer 27

Cool. I got answers on reddit, but they weren't very detailed (I just got a distribution graph of a similar problem which I posted, and the problem was quickly forgotten)

Answer 28

Can you pass me the link ? Reddit

Answer 29

Also, I forgot to add in the problem, I randomly guess with no bias to any choice.

Answer 30

Okay so you are just attempting blindly? (not solving)

Answer 31

http://www.reddit.com/r/cheatatmathhomework/comments/re6fv/high_school_probability/

Answer 32

For now, attempting blindly.
(I'll probably make up a bunch of variations on this problem, but I have no idea how to solve the first, so I'll just try to keep it simple)

Answer 33

When you have this kind of problem, this is best place to get your answers : http://math.stackexchange.com/

Answer 34

Is it that hard?

Answer 35

It could be you are adding lots of variations of you own, I often do that and sometime end up scratching open problems.

Answer 36

your*

Answer 37

fool, what was your sqrt x + sqrt y = sqrt a , problem, dealing with tangents , yesterday

Answer 38

The answer is a. perl

Answer 39

So, I could post it there without getting criticism for giving an elementary math problem?

Answer 40

nvm about that, I got the wrong site in mind

Answer 41

http://math.stackexchange.com/questions/81683/

Answer 42

http://math.stackexchange.com/questions/60726

Answer 43

http://math.stackexchange.com/questions/12587/

Answer 44

No lol users at math.stackexchange are very critical, be careful.

Answer 45

I don't think your problem is more elementary than them.

Also probablity distribution ain't elementary.

Answer 46

Ishaan I am an user and I ain't critical :P

Answer 47

fool, im talking about the problem you posted yesterday, about the tangent or something

Answer 48

the question above is a hypergeometric distribution , fool

Answer 49

I'll just hope it'll be too hard for them, and they won't make fun of me. :D

Answer 50

yes perl I know I have answered it.

Answer 51

the question you posted yesterday, i think its one of your special questions

Answer 52

you posted like 10 open questions

Answer 53

I mean most of the users or most of the active users.

Answer 54

They never make fun of anyone, if the problem is bad we would close it down

Answer 55

If I were you I would have posted it. I dont' really care what others thinks about me as long as I am learning ...;)

Answer 56

perl I know the answer is a.

Answer 57

Yes, you should post it.

Answer 58

You may like to add what have you tried so far. so that others may help you appropriately.

Answer 59

Done,
http://math.stackexchange.com/questions/127549/probability-distribution-im-pretty-sure-its-higher-than-high-school-math-but

Answer 60

+1 from me :)

Answer 61

thanks :D

Answer 62

By the way, how intertwined are statistics and other mathematics? (like graduate level I mean, I just want to have a general idea of what I will be learning if I major or minor in math)

Answer 63

well pretty much however I am not sure if any with analysis.

Answer 64

If the tangent the to the curve x√+y√=a√ at any point on cuts x-axis and y-axis at two distinct points. Can you find the sum of the intercepts ? Good luck!

Answer 65

perl, for the n'th time the answer is a

Answer 66

wait, how do I have a profile without registering? That's an awesome system.

Answer 67

i didnt ask the answer,

Answer 68

i just post the question, see ?

Answer 69

That's an Unregistered profile with limited privileges.

Answer 70

but i will work on it, give me a moment

Answer 71

as far as your conics question, you took the partial deriv because the slope is zero there

Answer 72

i have a 3d grapher, im trying to get a feel for this

Answer 73

Wow, answer already!

Answer 74

Assume the point to be \((x_0,y_0)\)
\[\frac{dy}{dx} = -\sqrt{\frac{y_o}{x_0}}\]Equation of tangent at point \((x_0,y_0)\) must be,
\[y - y_0 = -\sqrt{\frac{y_0}{x_0}}(x - x_0)\]
Get the intercept form of the equation and then add them up.
That's how I did it, but I would love to see a better way to do this.

Answer 75

That's how I did it too.

Answer 76

It's "definitely basic", but I don't understand a word of the explanation.

Answer 77

Lol

Answer 78

what is xo,yo? in your problem

Answer 79

Happens a lot to me, I don't understand most of the question on math.stackexchange :/
But don't worry, you just need to work hard and then in a year, you will be ruling math.stackexchange.

Answer 80

you are not given any (xo,yo)

Answer 81

a year ruling MSE? !! Dude those people are professors

Answer 82

I think I'll go back there after I finish college.

Answer 83

I assumed them to be a point on the curve for the point of contact.

Answer 84

it says two distinct points

Answer 85

I think a year might get me finished with calculus and differential equations (hopefully discrete and linear), but I want to learn so much more than just that.

Answer 86

maybe i misunderstand the question.
If the tangent the to the curve x√+y√=a√ at any point on cuts x-axis and y-axis at two distinct points. Can you find the sum of the intercepts ? ,
this is not grammatically correct

Answer 87

so (xo,yo) is the point on the curve that the tangent goes through , ok

Answer 88

the intercept form is
x/a + y/b = 1 , i believe

Answer 89

Not all, I have seen several guys just aged 16 or 17 with more than 1k+ points.
I think if one prepares for the IMO, he can easily answer most of the questions on math.stackexchange. Serious preparation.

Answer 90

Yes, that is the intercept form.

Answer 91

I mean't people with 10k+ rep.

Answer 92

and there are few exception here and there.

Answer 93

But 1k+ is not that hared.

Answer 94

so whats the next step

Answer 95

Oh hmm yeah probably 1k isn't that hard. I mean yeah, 10k+ and 1k+ huge difference. 10k+ is definitely hard.

Answer 96

Time to close this monster post xD

Answer 97

Get the equation of tangent.

Answer 98

Okay!