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Do "odds" really mean anything?

My favorite anecdote is that one evening while I was in college, I was doing my homework. Suddenly, our of nowhere, I had a thought about my grandmother, accompanied by concern for her health. Not 20 seconds later, my phone rang.


It was a wrong number.
 
UKBoy1977 said:
Just to be picky, Chulbert you expressed your odds the wrong way round. The odds of rolling a 6 on a fair die is 5/1, not 1/5!

I and every stats glossary I could Google in 3 minutes says I'm right. The odds against rolling a 6 is 5/1. The odds of rolling a 6 is 1/5.
 
Re: Re: Re: Re: Re: Do "odds" really mean anything?

Beausoleil said:


The same's lightly true of probability, in a way. Consider airplane statistics - some airlines have a crash every 1 million flights, some every 10 million flights. Is the latter 10 times safer?

Or do you look at the probability of a safe arrival, 0.9999990 vs. 0.9999999, making one airline 1.0000001 times safer than the other.

Yes, the latter is 10 times safer.
 
OK Chulbert I'll concede on this. I do a lot of gambling so I was thinking of gambling terminology.

The odds of throwing a 6 is 1/5 (which is 5/1 against in gambling terminology)
 
The odds of throwing a 6 is 1/5 (which is 5/1 against in gambling terminology)
The odds of throwing a 6 is 1/6 - which is 5 to 1 against in gambling terminology.

1/6 = 1 out of 6 = 1 to 5 in favor of = 5 to 1 against = 0.1666...
 
chulbert wrote:
I and every stats glossary I could Google in 3 minutes says I'm right. The odds against rolling a 6 is 5/1. The odds of rolling a 6 is 1/5.
You're both wrong. The odds of rolling a six is 1:5. "1/5" is a fraction equal to 0.2, and that's not what we're talking about here. You need to use the colon instead of the division sign.
 
CurtC said:
You're both wrong. The odds of rolling a six is 1:5. "1/5" is a fraction equal to 0.2, and that's not what we're talking about here. You need to use the colon instead of the division sign.

a:b = a/b
 
Fishbob has it right.

I assume you're talking about throwing one die which has six sides. Since only one side has a six the probablility of rolling a six is one out of six or 1/6. Expressed as odds this would be 5 to 1 or 5:1 against.

If you're talking about rolling a total of six while playing craps the probability is five out of thirty-six or 5/36. Expressed as odds this would be 31 to 5 or 31:5 against.

Probabilities are expressed as fractions or decimals showing the percentage of times you can expect success. Odds are the ratio of the possible losing outcomes to the winning outcomes.
 
fishbob said:

a:b = a / (a+b)

a/b does not = a / (a+b)

Depending on the context, a:b = a/b, or a:b = a/(a+b). It just depends on if you are talking about ratios or odds. :)
 
You got a cite for that, T'ai Chi, or is it your own personal notation system?

Let's talk about something other than odds. Let's dilute a substance, say vinegar, at a ratio (your example) of 1:2 with water. That's one part vinegar, two parts water. Vinegar makes up 1/3 of the mix. I know of no notation system where 1:2 would mean 1/2.
 
Although I'm not a numbers person (i.e. multiplication by 2 is quite a task for me to pull off), I am personally amused when people use "The odds were so high that it just couldnt have happened and therefore didnt happen" (search the web for those "1 in 600 million odds of DNA combining by chance" notations, you'll see what I mean)...

Ok, aside from that, I dont have much to add to this thread, sorry for wasting bandwidth...
 
CurtC said:
You got a cite for that, T'ai Chi, or is it your own personal notation system?


Here is one webpage: http://www.800score.com/gre-guidec7view1f.html, and here is another: http://www.oswego.org/staff/cchamber/math/grade5.htm, and: http://www.shodor.org/unchem/math/perc/


I know of no notation system where 1:2 would mean 1/2.

Mathematics..and anything that uses mathematics.

It is just that when people use a:b nowadays it mainly means 'odds', because a:b is taught as a ratio mainly, from what I can tell, in grade school.
 
This morning on the car radio, the DJ offered callers $10,000 if they correctly called 10 coin tosses. So the DJ flips the coin, and the caller takes his word about how the coin landed. Quickly figuring that the odds were 1 out of 2^10 (approx 0.001) if the flipper did not cheat, I decided not to waste my cell phone minutes calling in. The increased odds of crashing the car due to talking on the cell phone outweighed the potential winnings of the stupid contest.

The continuous line of callers, who had obviously not figured the odds, kept the DJ flipping until I got bored and changed the channel. The best guesser got 3 tosses before missing (1/8).

Do "odds" really mean anything?
The odds mean that I did not make a fool of myself today, yet.
 
CurtC said:
You got a cite for that, T'ai Chi, or is it your own personal notation system?

I don't have a bibliographical cite available, but my school mathematics textbooks for grades 4-9 book used : to denote division.
 
CurtC said:
You got a cite for that, T'ai Chi, or is it your own personal notation system?

Let's talk about something other than odds. Let's dilute a substance, say vinegar, at a ratio (your example) of 1:2 with water. That's one part vinegar, two parts water. Vinegar makes up 1/3 of the mix. I know of no notation system where 1:2 would mean 1/2.

How about the definition of rational? Any number than can be represented as the ratio of two integers.

If that's not enough, here are a few sites I found:

http://www.shodor.org/unchem/math/r_p/index.html
http://instech.tusd.k12.az.us/Core/glossary/mathglossary.htm
http://www.cde.ca.gov/standards/math/glossary.html
http://pax.st.usm.edu/cmi/inform_html/glossary.html#R
 
Well I can guarantee you that here in the UK, gambling odds are expressed using the / sign. So to translate from US odds:

-300 is expressed as 1/3

-150 is expressed as 4/6

+200 is expressed as 2/1

So my final word on it is that, in the UK at least :

The probability of rolling a 6 on a fair die is 1/6

This is odds of 1/5 (or 1:5 using the : notation)

Which is expressed as 5/1 against in gambling terms
 
UKboy1977---*I* have such coincidences, quite often. I actually started a journal of them. I have them at home though (which is 20 miles away). I could have something like this happen: I am in some plumbing stare discussing nursery rhymes with a worker, and then I will leave the store, and a particular nursery rhyme we were talking about would become whimsically added into a commentary on the radio..or I'd go home and read about how the originator of a particular nursery rhyme we were talking about, died today.

Or, for some reason, on a particular day, I decided to call someone a 'peckerhead'. A slang terminology from decades prior and one not hardly heard today. And I could return to my vehicle, turn on the radio, and one of the first things I hear on the radio is someone talk about 'peckerheads'. And I go. "What the...!"

Here is a real one that I can actually recall. My next door neighbors have two children. I see them all the time, and we all talk. One day I thumbed through something with a bunch of names on it, and when I glanced down, the names of the two kids were 'in order' out of all the names there...and...they were what I spotted first, in the middle of the page where I happened to be looking.

I told this story to someone I am close to, and they said to me, to one upsmanship me, that one day they were driving down the highway, and they spotted the childrens names on a rock out in front of these peoples house. Danielle and Brittany. The names of (the people I know) their grandchildren. And as we discussed and tried to look at this reasonably, this person said, "It's not as if when we drive down the road, we see all these signs with peoples names on them, and THIS time it happened to hit home in our case. And...how many people do you know, that only have two kids, and their names are Danielle, and Britanny/!"

With these kinds of coincidences, I don't think you can mathematically ascribe an actual odds. You might be able to take a stab at trying to approximate, based on certain data. You might say that you think it's less than one in a million, but probably higher than one in a thousand, based on no more than sheer guessing. But these types of occurances can cause oneself to consider that there is something at work here that we can't explain. And you try to guess whther or not the gods are trying to send you messages. Messages? Ya, like how we aren't as smart as we think we are...and events are controlled by someone/something more powerful than us.
 
Iamme:
With these kinds of coincidences, I don't think you can mathematically ascribe an actual odds. You might be able to take a stab at trying to approximate, based on certain data. You might say that you think it's less than one in a million, but probably higher than one in a thousand, based on no more than sheer guessing. But these types of occurances can cause oneself to consider that there is something at work here that we can't explain. And you try to guess whther or not the gods are trying to send you messages. Messages? Ya, like how we aren't as smart as we think we are...and events are controlled by someone/something more powerful than us.
Given the sheer number of types of events that we can consider to be coincidental, the odds of them NOT happening are astronomical, IMO.
 

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