# The Naked Scientists Forum

### Author Topic: How is probability calculated?  (Read 4961 times)

#### Thebox

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« Reply #25 on: 12/12/2015 17:28:26 »

There are also people on this site who believe that gravity is due to air pressure!!

We have explained the differences in the sequences between what you call X & Y, why they occur, and why they don't give the result you think they do.
We have never attempted to mislead you.

I don't consider you have discussed and explained any comparison of X and Y.

Would you say this was a discrete and continuous diagram when the x axis is in constant shuffle ? ,

If I asked you to pick any square from any x axis you have a 1/2 chance of white and a 1/2 chance of black.  But If I offered you a choice from  any Y axis, you can observe the physics is ?/? and 1/2 and that is the paradox I am trying to explain.
« Last Edit: 12/12/2015 17:38:36 by Thebox »

#### Thebox

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« Reply #26 on: 12/12/2015 19:50:30 »
To be honest I think I just want give up, I thank this forum as been one of the best and the mods are definite the best mods on the internet.  Thanks.

I thank the other members also, but for my own sanity and to stop my self coming on forums, will you please just ban me now for real.

#### Colin2B

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« Reply #27 on: 12/12/2015 21:39:42 »
We have been over the differences between X and Y in previous threads and the probabilities you have been shown are nothing new. I don't intend to go over old ground again and again.

Words like expectation, discrete, continuous have very specific meanings in probability.
Y like X is discrete because it cannot take any value just integers 1 to 52. A measurement like length is continuous because it can take any value. It is important you call things by their correct names otherwise you will always be misunderstood.

I wish you luck in your quest, but you might have better luck if you were looking for the Holy Grail.
Let us know how you get on with the gaming board.

Who should you trust?
Trust in God, but keep your powder dry.

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#### alancalverd

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« Reply #28 on: 13/12/2015 00:22:15 »
How many aces are there in these 52 random's.

My head feels like it is in the twilight zone....about 4?   where the hell do you get about 4 from? It is 79.7% chance that there is not 4, saying 4 is equivalent to predicting the lottery results.

You have picked 52 cards at random. Each one came from a full deck and thus had a 1 in 13 probability of being an ace. 52/13 = 4. This is the "expected" value, and if you repeated the experiment several times, you would expect the average number of aces to converge towards it. However there is obviously a finite probability that you could get any number from 0 to 52 aces in your selection, and that distribution is clearly skewed: the likelihood of 3 or 5 is larger than 2 or 6, but you can't get less than 0 (the probability of zero is (12/13)52= 1.5%), whilst the likelihood of 52 is (1/13)52 = 1.2 x 10-58 - nonzero but very small indeed.

Stating 4 would indeed be a bit like predicting the result of a lottery, which is why I said "about 4" - this is mathematically sensible and if I had to bet on any number, it would obviously be 4.

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#### Thebox

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« Reply #29 on: 13/12/2015 10:13:56 »
Thank you all, in the final question on this

have 52 decks of cards lined up, slide off the top card of each deck, like in the earlier scenario, then slide the cards back onto the top of the original decks, you are having the first card,

you are offered a choice of top card, would you agree that this changes things compared to using a single deck?

About 4 that changes every turn, is not the same has a constant 4.

Would you agree that X 4/52 is not equal to Y <,>,=4/52  less than, more than or equal to 4.

P(a)/x=4

p(a)/y=<,>,4=0

where (a) is any one of 4 different suits of a single value such has an ace, and X and Y =52

and added, the time problem.  Courtesy of Khan.

« Last Edit: 13/12/2015 11:00:15 by Thebox »

#### Thebox

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« Reply #30 on: 13/12/2015 11:09:03 »
My own pic of the time travelling into the future.

#### alancalverd

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##### Re: How is probability calculated?
« Reply #31 on: 13/12/2015 12:18:37 »
you are offered a choice of top card, would you agree that this changes things compared to using a single deck?
No. The probability of any top card being an ace remains at 1/13 because you haven't changed anything.

Quote
P(a)/x=4

p(a)/y=<,>,4=0
is obvious nonsense if P is a probability. No probability can exceed 1.

#### Thebox

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##### Re: How is probability calculated?
« Reply #32 on: 14/12/2015 11:29:59 »
you are offered a choice of top card, would you agree that this changes things compared to using a single deck?
No. The probability of any top card being an ace remains at 1/13 because you haven't changed anything.

Quote
P(a)/x=4

p(a)/y=<,>,4=0
is obvious nonsense if P is a probability. No probability can exceed 1.

Hi Alan, 4 was 400%, each individual ace being 100% itself.

You say 1/13, I am confused by this ,

a dice 1/6
a coin 1/2
a roulette wheel 1/37
a deck of cards  1/52
aces in a deck of cards 4/52

Where are you getting 1/13 from that would suggest a known odds/chance?

#### chiralSPO

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##### Re: How is probability calculated?
« Reply #33 on: 14/12/2015 15:23:52 »
4/52 = 1/13

#### Thebox

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##### Re: How is probability calculated?
« Reply #34 on: 14/12/2015 15:38:43 »
4/52 = 1/13

4/52 =4/52

1/13=1/13

4/52 is not equal to 1/13

I have not offered a choice of 13, I offered a choice of 52,

below 4 choices of X axis 1/13 and 4 choices of Y axis 4/4

Clearly there is something different in the x and y axis to output P's in this diagram

« Last Edit: 14/12/2015 15:53:07 by Thebox »

#### Colin2B

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##### Re: How is probability calculated?
« Reply #35 on: 14/12/2015 15:48:28 »
4/52 =4/52

1/13=1/13

4/52 is not equal to 1/13
This is an example of what is frustrating about you. You claim to know maths and probability, but fail to understand the most basic of the maths. This is why there are so many misunderstandings.
Probability, to answer your question, is measured by dividing the number of items (or cases) favourable to what you are trying to find, divided by the total number of possibilities (cases).This is a fraction, but is usually shown as a decimal number between 0 and 1.
So for a coin, if we want the probability of a head then there is one head (favourable case) but 2 possibilities head and tail. So probability is 1/2 as a fraction, or 0.5 as a decimal fraction, or 50% as a percentage. But fractions can be shown in different way so 1/2=2/4=4/8=8/16 so if you divide 8/16 you still get 0.5 as with 1/2, so they are all saying the same thing.

OK, I know you will say you knew all that, but your questions indicate you don't.

#### Thebox

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##### Re: How is probability calculated?
« Reply #36 on: 14/12/2015 15:55:38 »
4/52 =4/52

1/13=1/13

4/52 is not equal to 1/13
This is an example of what is frustrating about you. You claim to know maths and probability, but fail to understand the most basic of the maths. This is why there are so many misunderstandings.
Probability, to answer your question, is measured by dividing the number of items (or cases) favourable to what you are trying to find, divided by the total number of possibilities (cases).This is a fraction, but is usually shown as a decimal number between 0 and 1.
So for a coin, if we want the probability of a head then there is one head (favourable case) but 2 possibilities head and tail. So probability is 1/2 as a fraction, or 0.5 as a decimal fraction, or 50% as a percentage. But fractions can be shown in different way so 1/2=2/4=4/8=8/16 so if you divide 8/16 you still get 0.5 as with 1/2, so they are all saying the same thing.

OK, I know you will say you knew all that, but your questions indicate you don't.

No Colin I understand, the point is why are you removing something away, narrowing it down when the scenario of 52 has not contracted in any way.

example -  AAAA......1-13........52    there is no 1/13 in this example, the aces are aligned in the top 13.

I offered you 1 of 52 random cards, I did not offer you to pick 13 cards then pick one of them.
« Last Edit: 14/12/2015 15:59:22 by Thebox »

#### Colin2B

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##### Re: How is probability calculated?
« Reply #37 on: 14/12/2015 16:02:27 »
No one is removing anything. Do the sums
4/52=0.0769=7.69%.
1/13=0.0769=7.69%.
They are exactly the same.
If you don't get this you really don't understand maths and probability.

#### alancalverd

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##### Re: How is probability calculated?
« Reply #38 on: 14/12/2015 16:06:48 »

Where are you getting 1/13 from that would suggest a known odds/chance?

4/52 = 1/13 in my universe.

#### Thebox

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##### Re: How is probability calculated?
« Reply #39 on: 14/12/2015 16:11:18 »
No one is removing anything. Do the sums
4/52=0.0769=7.69%.
1/13=0.0769=7.69%.
They are exactly the same.
If you don't get this you really don't understand maths and probability.

I understand Colin, everybody seem's to be missing the point,

Take 52 top cards from 52 shuffled decks, forming new deck Y. Shuffle the Y deck, take the top card, look at it, the chance of that card being an ace is 4/52 or 1/13 or 7.69%, yes I agree with this but only if we know that there is exactly 4 aces in new deck Y.   There is only a 20.3% chance that Y contains exactly 4 aces, and an even less chance to be 4 individual aces.    There is a 1.6% chance there is no aces at all. There is a variable of percentage to how many aces Y contains.

Lets say you your top card is an ace from Y  , and its the ace of hearts.  draw the second card , what is the chance that card is also an ace, and also the ace of hearts?

It should be zero percent in a standard deck, premise for argument and discussion.

Draw the 20th card and the 34 th card, what is the chance they are also the ace of hearts?
« Last Edit: 14/12/2015 16:15:48 by Thebox »

#### Colin2B

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##### Re: How is probability calculated?
« Reply #40 on: 14/12/2015 16:39:43 »
everybody seem's to be missing the point,
No one is missing the point. You asked Alan a very specific question about expectation and he answered correctly.
if you look at the probability distribution of the number of aces in your constructed deck you will see that 4 aces has the highest probability, so over a large number of games you would expect to get around 4, same as for a standard deck.
If you look back at previous threads we have been over this before. We never said the sequences are the same, just that the long run probabilities are the same.

#### alancalverd

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##### Re: How is probability calculated?
« Reply #41 on: 14/12/2015 21:57:25 »

Take 52 top cards from 52 shuffled decks, forming new deck Y. Shuffle the Y deck, take the top card, look at it, the chance of that card being an ace is 4/52 or 1/13 or 7.69%,

No. The expectation value is 1/13, but unlike a proper deck, it is conceivable that the new deck contains anything from 0 to 52 aces, as you say.

Quote
Lets say you your top card is an ace from Y  , and its the ace of hearts.  draw the second card , what is the chance that card is also an ace, and also the ace of hearts?
1/52

#### The Naked Scientists Forum

##### Re: How is probability calculated?
« Reply #41 on: 14/12/2015 21:57:25 »