Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

probability on dice

A fair dice is tossed then find the probability that maximum of the two number is greater than

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: probability on dice

Another way of stating this problem is "find the probability that at least one of the two rolls is greater than 4".  The easiest way to solve this problem is to find the opposite, i.e. find the probability that neither roll is greater than 4.  With one roll there is a 4/6 = 2/3 chance that the roll is not greater than 4.  With two rolls you need both to be 4 or less, so the probability is 2/3 * 2/3 = 4/9.  This means there is a 4/9 chance that neither roll is greater than 4, so there is a 5/9 chance that at least one roll is greater than 4.

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Wrap it in bacon

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi juantheron;

When in trouble then do not be afraid to enumerate the entire sample space, or part of it.

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(4,5)(4,6)
(3,5)(3,6)
(2,5)(2,6)
(1,5)(1,6)

There are 20 correct answers. Each one can occur 1 / 36 of the time. 20 / 36 = 5 / 9.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: probability on dice

hi bobbym

is there any way to fin this numerically,for example in a case where the dice is thrown n times?

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi anonimnystefy;

I am not following you. If you ask for 15 times then you will get a number. If you ask for n times chances are you will get a expression involving n.

Which are you interested in?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: probability on dice

ok i get that.i'm asking if there's a formula to derive the number of 'correct answers' in the case of n dice being thrown?

---

“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi anonimnystefy;

Where n is the number of dice.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: probability on dice

how did you get that?

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi anonimnystefy;

By using the binomial distribution and then playing spot the pattern.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: probability on dice

wait i got it. couldn't we just take the opposite case (when all of the dice show a number less than or equal to four) then calculate the probability of that happening (which is (2/3)^n) and just go back to the original and doing : 1-whatwegot=1-(2/3)^n ???

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi;

Anyway that gets the right answer is fine.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: probability on dice

well not exactly.

example:

calculate 5+6

5=3+4
6=1+3

5+6=3+4+1+3=3+(4+1)+3=3+9+3=12+3=11

see what i mean?

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability on dice

Hi;

5=3+4

Step 1 is wrong.

What I am saying is there are many roads to getting the answer. In school you will be forced to use their methods. So your whole class will do things all the same way. Many will come to the conclusion that there is only 1 right way.

When you go to work, no one cares which method  or idea you use. Just get the right answer.

You gotta go with what works!

If your idea up there kept getting the right answer every time and not due to a priori, I would say keep doing what works.

Have you heard of the Feynmann quote?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.