You are not logged in.
#1 2012-12-14 07:11:28
- Festisio1
- Guest
[Discrete Math] Finals review problems in Probability
There are a couple of problems which even the discussion board on our University website has not answered:
A variation of the birthday problem:
Find the smallest number of people you need to choose at random so that the probability that at least two of them were both born on April 1 exceeds 1/2.
Suppose that the probability that x is in a list of n distinct integers is 2/3 and that it is equally likely that x equals any element in the list. Find the average number of comparisons used by the linear search algorithm to find x or to determine that it is not in the list.
Times like this, I wish i had the student solutions guide 
#2 2012-12-14 07:32:10
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
Hi
I am getting for the first problem and for the second problem.
Last edited by anonimnystefy (2012-12-14 08:01:01)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#3 2012-12-14 07:52:39
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi Festisio1;
A variation of the birthday problem:
Find the smallest number of people you need to choose at random so that the probability that at least two of them were both born on April 1 exceeds 1/2.
Assuming 365 days ( a non leap year ) you would need 253 people.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2012-12-14 07:54:24
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
Hi bobbym
They would need 613.
Last edited by anonimnystefy (2012-12-14 08:00:39)
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#5 2012-12-14 07:57:13
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
Not for a 365 day year.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2012-12-14 08:04:42
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
The probability that less than 2 people have their birthdays on April 1st is (364/365)^n+n*1/365*(364/365)^(n-1). This probability needs to be less than or equal to 1/2.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#7 2012-12-14 08:09:50
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
The probability of having the birthday April 1 is 1 / 365. The probability than n people do not have that birthday is
So solve:
n = 252.65 which is rounded to 253.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2012-12-14 08:12:15
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
You are not reading the question!
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-12-14 08:16:49
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
You are not reading the question!
You are right we are both not reading the question. The answer is 613.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#10 2012-12-14 08:20:08
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
Well, the expected number of people for two birthdays on the 1st of April cannot be less than for one birthday.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2012-12-14 08:24:21
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
You changed your answer to 613. So did I! That is correct.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#12 2012-12-14 08:25:54
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
Now it's okay. Though I changed it 25 minutes ago, and you didn't notice...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#13 2012-12-14 08:27:30
- Festisio
- Novice
Offline
Re: [Discrete Math] Finals review problems in Probability
For the birthday problem -- the book answer is 614 (book assumes 366 days a year)
I want to understand how to complete the problem.. the basic birthday concept, no prob -- but this variation is a little tough.
For the other problem, the book answer is
I have sheets and sheets of paper -- but I am not getting close -- I hate looking at the answer first, because I try to understand the concepts of obtaining them.. in these cases I could not find them
There again, I have been studying for 3 finals, which are tonight, and two more tomorrow, so I may be a little tired and missing things.
Last edited by Festisio (2012-12-14 08:29:02)
#14 2012-12-14 08:33:16
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
Yes, it is 614 for a leap year. It is not a birthday problem it is a binomial distribution problem.
That equation must be solved.
Hi anonimnystefy;
I was working on the problem so I did not notice.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#15 2012-12-14 08:34:50
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
Well, for the second problem, the book is wrong.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#17 2012-12-14 08:41:40
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi Festisio;
Discrete Math and its Applications?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#18 2012-12-14 08:59:37
- Festisio
- Novice
Offline
Re: [Discrete Math] Finals review problems in Probability
bobbym wrote:
Hi Festisio;
Discrete Math and its Applications?
Yes, that's correct.
McGraw has the 6th ed online here: http://highered.mcgraw-hill.com/sites/dl/free/0070648247/510610/Chapter_06_Discrete_Probability.pdf
It is page 440 #9 on there I don't know if they have the matching solutions.. but I am using the 7th edition..
Last edited by Festisio (2012-12-14 09:05:16)
#19 2012-12-14 09:01:34
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
For the 2nd problem I am getting
also.
I have sheets and sheets of paper -- but I am not getting close
I do not know about the 7th edition but the 6th edition has the answer to this problem just a few pages away!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#20 2012-12-14 09:16:50
- Festisio
- Novice
Offline
Re: [Discrete Math] Finals review problems in Probability
bobbym wrote:
Hi;
For the 2nd problem I am getting
also.I have sheets and sheets of paper -- but I am not getting close
I do not know about the 7th edition but the 6th edition has the answer to this problem just a few pages away!
I'm not understanding their examples.. I had to find help on Bayes' from youtube -- book does not even mention using a tree to simplify things..
Final is cumulative - no notes/calc anything .. there is just a vast amount of material. This last chaper (7) was basically assigned to us for finals week.. which means that we didn't really cover it.
#21 2012-12-14 09:27:07
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
Do you see example 8, entitled average case complexity of the linear search algorithm?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#23 2012-12-14 09:49:26
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
bobbym wrote:
Hi;
For the 2nd problem I am getting
also.I have sheets and sheets of paper -- but I am not getting close
I do not know about the 7th edition but the 6th edition has the answer to this problem just a few pages away!
How are you getting (4n+6)/3?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#24 2012-12-14 09:58:08
- bobbym
- Administrator
Online
Re: [Discrete Math] Finals review problems in Probability
Hi;
I am sorry, I am involved in forum matters and can not get to all the posts as quickly.
He has a derivation just 8 pages away from the question and it gives a formula.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#25 2012-12-14 10:06:54
- anonimnystefy
- Real Member
Offline
Re: [Discrete Math] Finals review problems in Probability
On which page is that?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón