[tonyC4L]

Anyone interested in a probability problem? I'm stumped.

A deck of 52 cards contains 4 aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all 4 aces will be received by the same player?

The answer is (4 * 13C4) / 52C4 (using nCr notation for "n choose r"), but I'm really having trouble interpreting that answer and seeing how to get it. I understand that it's written as (# of favorable outcomes) / (total # of outcomes) but I would think that the total number of outcomes would be 52!/(13!)^4, the number of ways to deal 52 cards to 4 people in groups of 13. I don't get where 52C4 comes from. If anyone has any advice or a hint or something I'd love to hear it.

[Spenny]

ffffffffuuuuuu calculus midterm tomorrow (Tuesday).

For some reason I'm really having troubles with derivatives. I get confused about when to use certain rules, and I have no fucking clue about the chain rule.

[DJWildefire]

Excited that we only have to do derivatives using the limit definition once or twice before we can switch to the "power rule"

[lbopm]

Originally Posted by tonyC4L

Anyone interested in a probability problem? I'm stumped.

A deck of 52 cards contains 4 aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all 4 aces will be received by the same player?

The answer is (4 * 13C4) / 52C4 (using nCr notation for "n choose r"), but I'm really having trouble interpreting that answer and seeing how to get it. I understand that it's written as (# of favorable outcomes) / (total # of outcomes) but I would think that the total number of outcomes would be 52!/(13!)^4, the number of ways to deal 52 cards to 4 people in groups of 13. I don't get where 52C4 comes from. If anyone has any advice or a hint or something I'd love to hear it.

They did write it a weird way. One thing to note is because of how choose is defined, 52c4 = 52c48

So think of it this way

we have 4 guys, hence 4* in front

now we want out of 13 cards, to have 4 cards be aces: (13c4)

now we assumed the 4 cards are acces, so that means we got 4 aces and then delt 48 more cards, so all the ways we can deal 48 cards is.. (52c48). This is weird to me as well, in fact I hate statistics, but... I will explain (try to anyway) how this gives the right answer as well:

So because choose does not depend on order, we can't find the ways to choose 52 cards from 52, which is 1 way, so we have to be more clever. We want a way to choose 48 cards, because we are asumming one of those ways leaves 4 aces left over (which are all together in someones hand). Now thats where (52c48) comes from. Now here is the weird part. Since order doesn't matter with choose, we need to make it matter by being clever. We want out of every 13 cards, the way to choose 4 cards. That way someone is going to have 4 aces (that's what we're choosing, the 4 aces). From here we only have to multiply the answer by 4 because there are 4 chances for this to happen.


Its very counter intuitive and probability is lame, but they yield the same answer.

[Spenny]

Is anyone knowledgeable with using the chain rule for derivatives? Anyone able to give me an example?

Or here, how about this question:

Find the derivative of the given function

f(x) = sqrt(x^2 + 1) / sqrt(x^2 - 1)

[Ben09]

Originally Posted by Spenny

Is anyone knowledgeable with using the chain rule for derivatives? Anyone able to give me an example?

Or here, how about this question:

Find the derivative of the given function

f(x) = sqrt(x^2 + 1) / sqrt(x^2 - 1)

You have to use the quotient and chain rule to get the final answer.

An easy example that shows the chain rule would something like (x^2+1)to the 1/2 (Or sqrt(x^2+1))

First you have to bring down the power and subtract by one giving you 1/2 * (x^2 +1) to the -1/2

Okay, inside the parentheses you have an x^2. That's something you can take the derivative of. There for you "chain out" a 2x.

Final answer being 2x * 1/2 * (x^2 + 1) to the -1/2 or x/sqrt(x^2+1)

Another example: Let's say you have ln(3x^2+x)

The derivative of ln is 1 over what's underneath. So you would have 1/(3x^2+x). But the stuff inside the parentheses "chains out" because you can take the derivative of it (6x +1).

So you're final answer would be 1/(3x^2 +x) *(6x+1), simplified to be (6x+1)/(3x^2+x)


Your problem:

((x-1)^1/2 *( (1/2 *(x^2+1)^-1/2 * 2x)) ) - ((x+1)^1/2 *((1/2 *(x^2-1)^-1/2 *2x)) ) all divided by (sqrt(x^2-1))^2

that's the answer to your problem without it being simplified. Not hard, it's just hard to keep track of some things. The 1/2's cancel because of the 2x's

[sdbrown]

Stats people- how would I find the approximation of a sample distribution? And then how would I go about finding a mean and std dev. for the approximation for the sample distribution?

I've basically tried everything to find this, I am going to fail statistics.

P.S. this site might be super helpful for some of you having trouble with calc --> www.Khanacademy.org

[Spenny]

Originally Posted by Ben09

You have to use the quotient and chain rule to get the final answer.

An easy example that shows the chain rule would something like (x^2+1)to the 1/2 (Or sqrt(x^2+1))

First you have to bring down the power and subtract by one giving you 1/2 * (x^2 +1) to the -1/2

Okay, inside the parentheses you have an x^2. That's something you can take the derivative of. There for you "chain out" a 2x.

Final answer being 2x * 1/2 * (x^2 + 1) to the -1/2 or x/sqrt(x^2+1)

Another example: Let's say you have ln(3x^2+x)

The derivative of ln is 1 over what's underneath. So you would have 1/(3x^2+x). But the stuff inside the parentheses "chains out" because you can take the derivative of it (6x +1).

So you're final answer would be 1/(3x^2 +x) *(6x+1), simplified to be (6x+1)/(3x^2+x)


Your problem:

((x-1)^1/2 *( (1/2 *(x^2+1)^-1/2 * 2x)) ) - ((x+1)^1/2 *((1/2 *(x^2-1)^-1/2 *2x)) ) all divided by (sqrt(x^2-1))^2

that's the answer to your problem without it being simplified. Not hard, it's just hard to keep track of some things. The 1/2's cancel because of the 2x's

Thanks :)

[tonyC4L]

Originally Posted by lbopm

They did write it a weird way. One thing to note is because of how choose is defined, 52c4 = 52c48

So think of it this way

we have 4 guys, hence 4* in front

now we want out of 13 cards, to have 4 cards be aces: (13c4)

now we assumed the 4 cards are acces, so that means we got 4 aces and then delt 48 more cards, so all the ways we can deal 48 cards is.. (52c48). This is weird to me as well, in fact I hate statistics, but... I will explain (try to anyway) how this gives the right answer as well:

So because choose does not depend on order, we can't find the ways to choose 52 cards from 52, which is 1 way, so we have to be more clever. We want a way to choose 48 cards, because we are asumming one of those ways leaves 4 aces left over (which are all together in someones hand). Now thats where (52c48) comes from. Now here is the weird part. Since order doesn't matter with choose, we need to make it matter by being clever. We want out of every 13 cards, the way to choose 4 cards. That way someone is going to have 4 aces (that's what we're choosing, the 4 aces). From here we only have to multiply the answer by 4 because there are 4 chances for this to happen.


Its very counter intuitive and probability is lame, but they yield the same answer.

Ugh that is really bizarre. I'm still not sure I fully understand it but thanks anyway lol

[stfu_man]

I have no clue why at twenty four I don't understand apparently simple math. I have been staring at this and did not get the answer the book provided. I am getting frustrated. Help!

Problem: The cost for making a telephone call from Vero Beach to Miami is 37 cents for the first three minutes and 9 cents per each additional minute. There is a 10% discount for calls placed after ten pm. What is the cost of a ten minute phone call placed at eleven pm.

The book gave an answer but didn't show the steps on how to get it. Thank you. Ugh.

[tonyC4L]

Originally Posted by stfu_man

I have no clue why at twenty four I don't understand apparently simple math. I have been staring at this and did not get the answer the book provided. I am getting frustrated. Help!

Problem: The cost for making a telephone call from Vero Beach to Miami is 37 cents for the first three minutes and 9 cents per each additional minute. There is a 10% discount for calls placed after ten pm. What is the cost of a ten minute phone call placed at eleven pm.

The book gave an answer but didn't show the steps on how to get it. Thank you. Ugh.

So you're given that this call is 10 minutes long and placed at 11 pm (so it get's the 10% discount). We'll come back to the discount part, since that's calculated once you calculate the cost of the phone call.

To do that, remember that the rate is 37 cents for the first three minutes and 9 cents per each additional minute. So for a 10 minute call, that's 37 cents for the first three and 9 cents each for the next seven. So the total cost of a 10 minute phone call (in cents) is 37 + (9 * 7) = 37 + 63 = 100. So the call costs 100 cents before any discounts are considered. Now look at the discount; since it's after 10pm, take 10% off of 100 cents, which is (0.9 * 100) = 90 cents. So the call costs 90 cents altogether.

Hope that explains it a little better.

[stfu_man]

Originally Posted by tonyC4L

So you're given that this call is 10 minutes long and placed at 11 pm (so it get's the 10% discount). We'll come back to the discount part, since that's calculated once you calculate the cost of the phone call.

To do that, remember that the rate is 37 cents for the first three minutes and 9 cents per each additional minute. So for a 10 minute call, that's 37 cents for the first three and 9 cents each for the next seven. So the total cost of a 10 minute phone call (in cents) is 37 + (9 * 7) = 37 + 63 = 100. So the call costs 100 cents before any discounts are considered. Now look at the discount; since it's after 10pm, take 10% off of 100 cents, which is (0.9 * 100) = 90 cents. So the call costs 90 cents altogether.

Hope that explains it a little better.

That's exactly what I did and that's exactly what I got however the book says the answer is $1.57! So can I assume this is a typo and stop stressing?

[bandnamexmyname]

A kid in my school aced the math SAT in fifth grade and utterly disgraced himself on Jimmy Kimmel.

[tonyC4L]

Originally Posted by stfu_man

That's exactly what I did and that's exactly what I got however the book says the answer is $1.57! So can I assume this is a typo and stop stressing?

Oh yeah that seems like a typo then. I hate when that happens lol

[stfu_man]

Originally Posted by tonyC4L

Oh yeah that seems like a typo then. I hate when that happens lol

Okay I am glad I posted this and I am glad it wasn't me. Can I PM you if I have any other questions? Hehe. Thanks for the help, dude!