Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-04-13 01:20:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Cookies!

In a cookie jar, there are 6 chocolate chip cookies and 8 oatmeal cookies. Hungry Paddy takes out the cookies one at a time and proceeds to eat them. The probability that the 7th cookie that Paddy eats is a chocolate chip cookie is a/b, where a and b are positive coprime integers. What is the value of a+b?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#2 2013-04-13 01:42:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#3 2013-04-13 01:44:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

Thanks but how to do?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#4 2013-04-13 01:58:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

Hi;

This sort of tells you it doesn't matter what number you pick to eat a chocolate chip cookie.

Actually this is a trick question and no computation at all is required to solve it.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#5 2013-04-14 00:02:03

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

How did you get into that formula?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#6 2013-04-14 00:04:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

It is really just a joke but I used the box model. It is unnecessary!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#7 2013-04-14 00:15:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

Why should it be a joke?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#8 2013-04-14 00:22:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

Because it is a trick question and using a computational idea on it just shows how stupid I am.

I ask you this what is the probability that the 15 th card from the top of a standard deck is a 5?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#9 2013-04-14 00:53:38

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

So how do you answer that question? I am still clueless


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#10 2013-04-14 00:57:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

What is the chance that the top card of the deck is a 5?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#11 2013-04-14 01:03:48

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

1/52


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#12 2013-04-14 01:07:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

That would be a particular 5 like the 5 of spades. There are 4 fives. Please recompute the answer.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#13 2013-04-14 01:17:06

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

1/13 ?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#14 2013-04-14 01:18:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

That is correct. Now you see that the 15th card is just the same as the top card.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#15 2013-04-14 01:22:52

Nehushtan
Member
From: London
Registered: 2013-03-09
Posts: 612
Website

Re: Cookies!

bobbym wrote:

Because it is a trick question and using a computational idea on it just shows how stupid I am.

You’re not alone. I was tricked as well. rolleyes


154 books currently added on Goodreads

Offline

#16 2013-04-14 01:28:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

If someone phrases the question a little bit different, I bring in the heavy machinery. No wonder my back is bad.

Confucius says,"Don't use a cannon to kill a mosquito."


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#17 2013-04-14 02:07:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

The fiftteenth card isn't the same as the first. If any of the previous fourteen were a five, then the fifteenth could not have been a five


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#18 2013-04-14 02:10:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

You have no information like that. The 15th card has the same amount of information that the first card has. For instance, if I count down to the 15 th card and put it on top has it's probability changed?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#19 2013-04-14 02:11:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Cookies!

I am intrigued by this problem.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#20 2013-04-14 02:14:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

Just understand that it is the card problem reworded. It can be verified by the above calculation or by enumeration. The probability is always the same.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#21 2013-04-14 02:20:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Cookies!

Yes, I know. I read the discussion.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#22 2013-04-14 02:23:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,362

Re: Cookies!

I just have to convince Agnishom and he can be a toughie.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#23 2013-04-14 02:28:13

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

bobbym wrote:

The fifteenth card has the same amound of information

Nope. When you have gone down to the fifteenth card you already have the information of the fourteen cards above

Last edited by Agnishom (2013-04-14 02:29:00)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#24 2013-04-14 02:29:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Cookies!

What information do you have about it? You do not look at the first 14 cards.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#25 2013-04-14 02:33:10

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,252
Website

Re: Cookies!

There are many different ways in which it can turn out to be a five.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

Board footer

Powered by FluxBB