# This doesn't make sense to me

#### The Game

##### New Member

"Just because something is the most probable outcome doesn’t mean it is the most likely outcome; you can have unlikely outcomes that are still the most probable."

How can something that is the most probable outcome not be the most likely and how can an unlikely outcomes(s) still be the most probable?

Thank you.

#### noetsi

##### Fortran must die
Those comments make no sense to me, since I define probable and likely the same. Where does the quote come from, they apparently don't define probable to be the same as likely or else they would not be making this comment.

#### The Game

##### New Member
Those comments make no sense to me, since I define probable and likely the same. Where does the quote come from, they apparently don't define probable to be the same as likely or else they would not be making this comment.
The origin of the quote is one of the main problems. I am unsure of where it came from as I have it in my notes but didn't write down the source. I think it was from a podcast and I remember the source seeming very credible and that is why I scratched my head and wrote down what he said.

I am going to try to google the quote again and see if I can find it in writing anywhere.

#### bryangoodrich

##### Probably A Mammal
On the face of it, I'd say that's nonsense; without context, who knows what the author meant by "probability" and "likelihood." Clearly, the naive and basic definition of probability is likelihood, especially defined as the simple proportion of the event given all other possibilities--and if this space be infinite, we use calculus.

#### noetsi

##### Fortran must die
A basic problem with writing down comments, especially in handwriting, is that you can be completely baffled by it later. I know this from very painful experience....

#### Mean Joe

##### TS Contributor
I'll make a guess.

"Just because something is the most probable outcome doesn’t mean it is the most likely outcome; you can have unlikely outcomes that are still the most probable."

Say you have 3 outcomes. P(outcome A) = 0.40, P(outcome B) = 0.30, P(outcome C) = 0.30.
Outcome A is the most probable, but is not the most likely -- IF you think of "not A" as being more likely than A.

Basically I'm thinking that the meaning of "likely" is that its probability is greater than 50%.

You can have unlikely outcomes (say P(outcome A)=0.05) that are still the most probable (say 95 other outcomes each with P=0.01).

#### Jake

I think either the person misspoke or you accidentally transcribed it wrong. As stated, it doesn't make sense. But what I suspect the person was trying to say was (change is in bold/underline):

"Just because something is the most probable outcome doesn’t mean that it is actually likely to happen; you can have unlikely outcomes that are still the most probable."

We can clearly see that this edited version is true in the simple example of rolling two fair dice and adding up their results. There are eleven possible outcomes here: we could get as low as 2, or as high as 12. The most probable outcome would be to obtain a 7. However, even this most probable outcome only has a 1 in 6 chance of occurring (there are six ways to roll a 7, out of thirty-six possible combinations of die faces). Most would not consider 1 in 6 to be particularly likely.

#### The Game

##### New Member
A basic problem with writing down comments, especially in handwriting, is that you can be completely baffled by it later. I know this from very painful experience....

#### The Game

##### New Member
I'll make a guess.

"Just because something is the most probable outcome doesn’t mean it is the most likely outcome; you can have unlikely outcomes that are still the most probable."

Say you have 3 outcomes. P(outcome A) = 0.40, P(outcome B) = 0.30, P(outcome C) = 0.30.
Outcome A is the most probable, but is not the most likely -- IF you think of "not A" as being more likely than A.

Basically I'm thinking that the meaning of "likely" is that its probability is greater than 50%.

You can have unlikely outcomes (say P(outcome A)=0.05) that are still the most probable (say 95 other outcomes each with P=0.01).
Good Guess.

That is what he was talking about; the combined probabilities of the the "other" outcomes outweighing the most "likely" or probable one (which he did define as greater than 50%).

Thank you.

#### The Game

##### New Member
I think either the person misspoke or you accidentally transcribed it wrong. As stated, it doesn't make sense. But what I suspect the person was trying to say was (change is in bold/underline):

"Just because something is the most probable outcome doesn’t mean that it is actually likely to happen; you can have unlikely outcomes that are still the most probable."

We can clearly see that this edited version is true in the simple example of rolling two fair dice and adding up their results. There are eleven possible outcomes here: we could get as low as 2, or as high as 12. The most probable outcome would be to obtain a 7. However, even this most probable outcome only has a 1 in 6 chance of occurring (there are six ways to roll a 7, out of thirty-six possible combinations of die faces). Most would not consider 1 in 6 to be particularly likely.
Your response jogged my memory and the dice example was actually the one used to illustrate the point. Here is the next bullet point I found in my paper notes (I transcribe them to microsoft word).

"Likely = more than half a chance but 7 is still the most likely score in a 2 pair dice toss."

There may have been a transcribing error or perhaps the politics of ellipsis are to blame

Thank you Jake.

Sorry just getting back to all you guys now but was determined to find these notes buried in my notebooks.