Thanks guys its starting to come together for me

we have an infinite number of cards, each with a number from 1 to 92 printed on them. Each number has an equal 1/92 probability of being printed. we draw 92 cards, and want to know the probability that our 92 card set contains at least one of each of 4 specific numbers.

(1 - ((88^92) / (92^92))) * (1 - ((89^91) / (92^91))) * (1 - ((90^90) / (92^90))) * (1 - ((91^89) / (92^89))) = 0.501130861

what am i double counting?

What do you think those numbers represent?

1-conditional prob of not getting the card. so we have 1 - p(drawing 92 cards that dont contain one of the 4)*(1-p(drawing 91 cards that dont contain any of the remaining 3)....

so for example 1 - ((88^92) / (92^92)) because theres 88 cards that arent desired, were choosing 92 cards, divided by total possiblities of 92 possible cards 92 times. no good?

So you're drawing 92 cards, then 91, then 90, then 89?

no im drawing 92 straight, but my understanding was you need to first find p(set contains 1), then conditional p(subset contains 1) and so forth.

So, what are you conditioning on? I'd just like you to write out in words what you think each of the probabilities you wrote above actually represents. Since you used the word "conditional" you can say something like "probability of <event occurring> given <event occurring>"

conditional probability of 91 card subset containing one of our desired cards given that original 92 card set contains one of our desired cards.

Here's what I want:

where you can list X1, X2, etc in words.

Then start to do the math and try to compute as many of those things as possible.

ok i think youve confused me because thats what i thought i wrote. lets start simple:

if we just choose one card, probability we see it in a 92 card draw is 1 - ((91^92) / (92^92)) = 0.634129008, because we are finding the probability we dont see it so we have 91 cards out of 92, 92 times. is that accurate?

yup

ok, now, expanding on that, we do the 2 card scenario:

1 - ((90^92) / (92^92)) = 0.867617447 is the probability that the set contains either card and

1 - ((91^91) / (92^91)) = 0.630108448 is the probability given that the 92 card set contains either card, the remaining 91 cards contains one. multiplying:

(1 - ((90^92) / (92^92))) * (1 - ((91^91) / (92^91))) = 0.546693083

but, this doesnt account for when the 2nd card is the same as the first which will be half the time since they are equally probable, so should i divide the 2nd probability by 2?

or rather, multiply by 1/2, which means when i expand to the 3 card scenario i have to multiply the 3rd probability equation by 1/3 to account for the 2/3 times when the third card is one of the first two. am i on the right track?

No, this is not correct (* at least it doesn't seem correct to me, but I will look at it hopefully more this afternoon/evening).

I can do it right, but it's super ugly and involves a ****load of sums. Let me think about a clean way to do this.

yea its really complicated, i am going to model it in excel and then compare results. if u can think of a clean way please post. i thought this would be trivial and now my head hurts.

Ah, was looking at it backwards. Just talked it out with a friend.

The probability of seeing all 4 is

1 - probability that you're missing one

= 1 - C(4,1) * (91/92)^92 [the C(4,1) is choosing which one you're missing]
but this overcounts, because if you're missing 2 of the guys, you've double counted

Point is, this is straight inclusion exclusion:

1 - C(4,1) (91/92)^92 + C(4,2) (90/92)^92 - C(4,3) (89/92)^92 + C(4,4) (88/92)^92

can you write an english translation of that forumula? i see:

1-(prob u miss one)*(number of ways to miss one) + (prob u miss 2)*(number of ways to miss 2) - (prob u miss 3)*(number of ways to miss 3) + (prob u miss 4)*(number of ways to miss 4)

why is the sign switched on the miss 3?

http://en.wikipedia.org/wiki/Inclusi...sion_principle

"# of ways to miss one" double counts all the times you're missing 2 (it counts them once under "missing #1" and once under "missing #2").

So you have to add back in the ways you can be missing 2 guys. Oh, but you now have a problem with how you've counted situations where you're missing 3 guys...and so on.

i was considering such a problem when dealing with a numerics issue a while back and i found that since you essentially flip the graph over the x=y line to get the inverse function, we can think of the derivative of dy/dx as a vector [dy dx]

then do the matrix the flips over y=x and get [dx dy] then inpret that as the flipping of a fraction and getting 1/f'(x) = d/dx (f_inv(x)).

then i was thinking you could use this to model the movement of a functions root along a function f(x) + e along the x-axis by doing like the (root of f(x)) + 1/integral(root,root+e)(f'(x))dx or (root of f(x)) + integral(root,root+e)(1/f'(x)dx) or something of the like. is there anything i should look into involving this?

Hi guys I have a quick physics question involving magnetic fields through a loop.

Here it is:

If you have an increasing magnetic field that is pointing into the page (through a loop) what will the direction of the current be?

Also, what would the direction of the current be if the magnetic field is decreasing.

(I'm just having a hard time understanding the right hand rule because from what I understand is if the magnetic field is pointing into the page the current should be traveling in the clockwise direction, but i have a feeling i am totally wrong.)

I'm still having problems with this guys, can someone help me out because I can't ask my professor since classes ended last week, but I still would like to know for my next physics class next quarter.

If the field is into the page and increasing then the the induced current wants to be counter clockwise because the magnetic field of the induced current wants to oppose the change. You can figure out the direction of the induced magnetic field from the right hand rule. Think about what happens to the magnetic flux if the magnetic field is decreasing then figure out which way the induced current needs to be in in order to oppose the change in magnetic flux.

seems like you should be able to solve this analytically?

flip ys for xs then natural log it. and you have your function... take deriviative. what am i missing?

Someone mind checking me on this

(4a/3ab^2) + (b/a^2c)

=[4a(a^2c)+b(3ab^2)]/[(a^2c)(3ab^2)]
=(4a^3c + 3ab^3)/[(a^2c)(3ab^2)]
=a(4a^2c+3b^3)/(3a^3b^2c)
=a(4a^2c+3b^3)/a(3a^2b^2c)
= (4a^2c+3b^3)/(3a^2b^2c)

Anyone here good at Psychology? Stuck on this question:

According to Konrad Lorenz, why do most people find viewing the act of a husband beating his wife as worse than watching scud missiles bomb Iraq?
Answer

In the missile attack, a national wrong is being righted, while in the case of the husband and wife, the argument is most likely much more gray.

In the missile attack, most of the destruction will be of property and therefore, while it is sad, it seems less violent.

In the missile attack, people’s empathic distress responses are activated and they are therefore better able to understand the actions being taken.

In the missile attack, people cannot see the victims suffer and therefore their natural inhibitors are not activated.