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Converting probability to odds

johnbarrymore

New member
Joined
Jan 26, 2018
Messages
1
Having problems converting some probabilities into odds. Need to turn these probabilities into odds as "1 in X chance"

0.192
0.01408
0.00128
0.000192
0.00000256
0.00000128
0.000000256

I thought it was just 1/probability, but that doesnt seem to be the case. Can someone figure them out then explain to me how they were done? Greatly appreciated!
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,089
Having problems converting some probabilities into odds. Need to turn these probabilities into odds as "1 in X chance"

0.192
0.01408
0.00128
0.000192
0.00000256
0.00000128
0.000000256

I thought it was just 1/probability, but that doesnt seem to be the case. Can someone figure them out then explain to me how they were done? Greatly appreciated!
Please do a google search on:

Difference between probability and odds.

Please tell us - what you find.
 

j-astron

Junior Member
Joined
Jan 10, 2018
Messages
181
Having problems converting some probabilities into odds. Need to turn these probabilities into odds as "1 in X chance"

0.192
0.01408
0.00128
0.000192
0.00000256
0.00000128
0.000000256

I thought it was just 1/probability, but that doesnt seem to be the case. Can someone figure them out then explain to me how they were done? Greatly appreciated!
If the odds are 1 (chance) in 100 that something will happen, that means the fraction of the time that you can expect it to occur (i.e. the probability, basically) is 1/100th the time. Probability = 1/100 = 0.01. Does this help illustrate the relationship between the two terms?
 
Last edited:

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
2,754
If the odds are 1 (chance) in 100 that something will happen, that means the fraction of the time that you can expect it to occur (i.e. the probability, basically) is 1/100th the time. Probability = 1/100 = 0.01. Does this help illustrate the relationship between the two terms?
Not quite; the terminology is a little different. See here.

If the probability is 1/100, which means 1 in 100, or 1 out of 100, then for every 1 way to win, there are 99 ways to lose. We say the odds against winning are 99:1 (99 to 1), and the odds in favor of winning are 1:99 (1 to 99).

People often mix up the two terms.

johnbarrymore, can you see how to apply this to your decimals, by first writing them as fraction?
 

j-astron

Junior Member
Joined
Jan 10, 2018
Messages
181
Not quite; the terminology is a little different. See here.

If the probability is 1/100, which means 1 in 100, or 1 out of 100, then for every 1 way to win, there are 99 ways to lose. We say the odds against winning are 99:1 (99 to 1), and the odds in favor of winning are 1:99 (1 to 99).

People often mix up the two terms.

johnbarrymore, can you see how to apply this to your decimals, by first writing them as fraction?
Oh, well that's interesting, and super annoying terminology. Anyway, sorry for adding more confusion. People use odds and probability interchangeably in everyday speech, so I'm pretty unclear on this now. When C-3PO (Empire Strikes Back) said the odds of successfully navigating an asteroid field were 3720 to 1, I always assumed their probability of success was 1/3720, but you're saying it was 1/3721. Again that's...annoying.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
2,754
Having problems converting some probabilities into odds. Need to turn these probabilities into odds as "1 in X chance"

0.192
0.01408
0.00128
0.000192
0.00000256
0.00000128
0.000000256

I thought it was just 1/probability, but that doesnt seem to be the case. Can someone figure them out then explain to me how they were done? Greatly appreciated!
Having just pointed out that people often confuse the terms "odds" and "probability", we have to make sure we know what you were told to do.

If you were told to find odds, then it will not be "1 in X" but "1 to X". How was the exercise actually worded?

If you were told to put the probabilities in the form "1 in X", then that is a probability, not odds.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
2,754
Oh, well that's interesting, and super annoying terminology. Anyway, sorry for adding more confusion. People use odds and probability interchangeably in everyday speech, so I'm pretty unclear on this now. When C-3PO (Empire Strikes Back) said the odds of successfully navigating an asteroid field were 3720 to 1, I always assumed their probability of success was 1/3720, but you're saying it was 1/3721. Again that's...annoying.
Exactly.

It might be worth noting that, first, the idea of odds probably started with gamblers rather than mathematicians (though in fact probability theory was invented by mathematicians who were gamblers!); and, second, odds have a purpose: to determine appropriate bets. If you bet according to the odds, then your expected value (your gain in the long run) will be 0 (you come out even).

So there's a reason behind it all. The trouble, as you say, is that people who don't understand either probability or odds keep getting it wrong, and mess up everyone else.
 
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