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#1 2014-04-01 22:56:41

iLloyd054
Member
Registered: 2014-04-01
Posts: 10

Probability Problem

1.
a.)    Your instructor gives the class a surprise four-question with 3-choice quiz. You have not studied the material being quizzed and therefore decide to answer the four questions by randomly guessing the answers without reading the questions or the answers.
Calculate
i)    what is the probability that you have more than half of the answers correct?
ii)    what do you think the class “average” number of correct answers will be, if an entire class answers the quiz by guessing ?

b)    The incomes of senior executive in a large corporation are normally distributed with a standard deviation of RM 1200. A cutback is pending, at which time those who earn less RM 28,000 will be discharged. If such a cut represents 5% of the junior executives, what is the current mean salary of the group of senior executives?

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#2 2014-04-01 23:28:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

Hi;

a)

b)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-04-02 08:59:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,883

Re: Probability Problem

Hi

I am actually getting 7/81 for a)i), bobbym. Are you sure you are counting only the cases with 3 and 4 correct answers?


“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

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#4 2014-04-02 09:02:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

Yes, I am counting 3, and 4 correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2014-04-02 09:08:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,883

Re: Probability Problem

What do you get for 3?


“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

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#6 2014-04-02 09:11:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

8 / 81

If you want to do this in M:

d = BinomialDistribution[4, 1/3];
Probability[x > 2, x \[Distributed] d]

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2014-04-02 09:17:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,883

Re: Probability Problem

How are you getting that?


“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

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#8 2014-04-02 09:19:07

ShivamS
Member
Registered: 2011-02-07
Posts: 3,459

Re: Probability Problem

Bobbym, your code does not work by the way.

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#9 2014-04-02 09:21:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

Did you copy and paste? It works fine here.

Hi anonimnystefy, this is a straight binomial distribution problem. The distributions of statistics are even more powerful then gf's for solving problems and M knows all about them.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2014-04-02 09:31:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,883

Re: Probability Problem

Hi bobbym

I made the mistake in taking the Binomial[4,3] to be 3 when doing it by hand.


“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

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#11 2014-04-02 09:37:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

But of course my young friend. If someone's answer disagrees with mine then I automatically know it is incorrect.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2014-04-02 10:00:00

ElainaVW
Member
Registered: 2013-04-29
Posts: 279

Re: Probability Problem

Keep joking with him like that and he isn't going to be your friend long. Why must you always tease the people you like?

The multivariable generating function can also be used.

The probability is 1 / 9.

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#13 2014-04-02 10:01:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

Well, I never teased you...

You are correct about the gf though.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#14 2014-04-02 10:06:13

ElainaVW
Member
Registered: 2013-04-29
Posts: 279

Re: Probability Problem

Sure you wanted to go into that in the other thread? smile I mean about the artificial intelligence work. You are correct and all but young people should not be exposed to different viewpoints. It will confuse them.

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#15 2014-04-02 10:09:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

I could not disagree more. pappym and grandpappyd exposed me to much of what I know to be true now when I was much younger than him. I expect his reaction will be disbelief and dismissal same as mine was but young people can handle differing opinions easier than you think.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#16 2014-04-02 10:13:23

ElainaVW
Member
Registered: 2013-04-29
Posts: 279

Re: Probability Problem

How will you handle the rest of the posted problems? smile

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#17 2014-04-02 10:14:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,980

Re: Probability Problem

They look like homework so I will start to stress to the OP the importance of at least trying to solve a problem before asking for help.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#18 2014-04-02 11:10:15

eigenguy
Member
Registered: 2014-03-18
Posts: 78

Re: Probability Problem

A different approach.


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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