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 2014-06-24 09:32:45

alake74895
Guest

Help with Probability problems

Can anyone give me some help on these problems?

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 10^{10}?

The four jacks, queens, and kings from a standard deck of cards are shuffled, and three cards are dealt to each of four players. Compute the probability that each player gets one jack, one queen, and one king.

Should I use constructive counting to solve these problems?

#2 2014-06-24 11:56:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

Hi;

The four jacks, queens, and kings from a standard deck of cards are shuffled, and three cards are dealt to each of four players. Compute the probability that each player gets one jack, one queen, and one king.

I am getting,


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#3 2014-06-24 12:11:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

What are you getting for the first one?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#4 2014-06-24 12:22:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

That is correct, I just finished it!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#5 2014-06-24 12:58:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Hi bobbyn

I'm getting twice your answer for the second one.


“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
The knowledge of some things as a function of age is a delta function.

Offline

#6 2014-06-24 13:16:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

I'm getting twice your answer for the second one.

Then divide by 2.


Seriously, I have done it in 2 ways. One was by actual count.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#7 2014-06-24 13:20:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

How many cases do you have when they get one each?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#8 2014-06-24 13:23:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

I am not following you? Do you mean a JQK?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9 2014-06-24 13:26:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Yep.


“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
The knowledge of some things as a function of age is a delta function.

Offline

#10 2014-06-24 13:31:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

There are 1296 of those exactly.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#11 2014-06-24 13:37:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

How are you getting that? I am getting 13824.

Maybe you are regarding the players as being the same?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#12 2014-06-24 13:40:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

Yes, I am regarding them as the same.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#13 2014-06-24 13:46:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Hm, something tells me that shouldn't change the outcome, though.


“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
The knowledge of some things as a function of age is a delta function.

Offline

#14 2014-06-24 13:47:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

If we regard them as 4 different players then I would multiply by 24.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#15 2014-06-24 13:50:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

I know. What do you get for total?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#16 2014-06-24 13:53:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

Total number of ways is a Mississippi problem.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#17 2014-06-24 13:54:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

What do you get? And what do you get when they're different players.


“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
The knowledge of some things as a function of age is a delta function.

Offline

#18 2014-06-24 14:01:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

This is the number of ways to put the 12 cards in a line. Then I just partitioned each group of 12 into 4 groups of 3.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#19 2014-06-24 14:07:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Is that with same or different players?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#20 2014-06-24 14:16:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

That counts the cards not the players.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#21 2014-06-24 14:33:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Did you divide your two numbers?


“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
The knowledge of some things as a function of age is a delta function.

Offline

#22 2014-06-24 14:42:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

Yes, these are the two analytical methods:


Going to eat, see you later.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#23 2014-06-24 21:51:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Ah, I see where else we differ. I differ between the suits.


“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
The knowledge of some things as a function of age is a delta function.

Offline

#24 2014-06-24 21:55:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 93,925

Re: Help with Probability problems

I solved it in 3 ways but each one is dependent on how I view the problem. If that is wrong then...


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#25 2014-06-24 23:15:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,918

Re: Help with Probability problems

Yes, the problem is not well-defined. We should wait for the OP to clarify, if he's able to.


“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
The knowledge of some things as a function of age is a delta function.

Offline

Board footer

Powered by FluxBB