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I wrote:

  1. Due to the symmetrical positions, there is same probability in selection of the destination node.

  2. Due to the symmetrical positions, there is equal probability to select the destination node.

  3. Due to the symmetrical positions, they (the nodes) have the same probability to be selected.


Info: We want to select a node among multiple nodes. The selection rule is a random variable and completely depends on the nodes' positions - the same position translates to the same probability of being selected. The selected node is called "destination node". We know the nodes have symmetrical positions. Consequently, probability of node 1 to be selected is equal with node 2, node 3, ...

Edit (Additional Information) :

The context is mathematics. Thus, probability is preferable rather chance and possibility.


Q1 : I want to convey that "the nodes have equal chance to be selected as the destination node". Now, which above sentence convey the same information?

Q2 : The main problem is how to use "the same/equal" and "have/there" in a sentence correctly.

Q3 : If all the sentences sound awkward, I will appreciate any hint or guidance.

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Actually, none of the three is usable as-is, but any of them could be made usable, with a bit of work. Starting with your sentence #1:

  • ...there is same probabiliy in selection...

This has two problems: first, you need the definite article "the" before "same": ...the same probability..

Second, it's not clear what "same" refers to. "same probability in selection..." Same as what? Something mentioned previously? No, each node's probability is the same as each other node. But you can't just say "each other" because the sentence does not mention the "nodes" from which the destination node is to be selected! So you need to mention them.

  • ...there is the same probability for each node in selection of the destination node.

Still not elegant. It doesn't make clear that one of the nodes must be selected to be the destination node.

Let's move on to #2:

  • ..there is equal probability to select the destination node.

In this one you need an indefinite article: "an equal probability".

Also, the phrasing "probability to select" is not idiomatic. You can say "equally likely to..." but not "{same/equal} probability to..." You need to say "probability of [something]. The [something] must be nounal, so use the gerund form "selecting".

Like so:

  • ..there is an equal probability of selecting the destination node.

Somehow, this doesn't seem accurate. If a destination node is sure to be selected, there is a 100% probability of "selecting the destination node. We really mean there's an equal probability for any node, but (as in #1) you didn't mention the "nodes"!

You could mention the nodes like this:

  • ..there is an equal probability of selecting any of the nodes as the destination node.

Oops... This is still active voice, and we failed to say who/what does the selecting. When you say "to select", this is active voice —you have to specify what (subject) is selecting what (object). And you didn't, and I infer you didn't want to mention, in this sentence, \who or what does the selecting_. Maybe it is clear in context, but you did not give surrounding context. So to get around mentioning who/what does the selecting, try passive voice (with the necessary inversion),

thus:

  • ..there is an equal probability of any of the nodes being selected as the destination node.

Better than #1.

Let's see what we can do with #3.

  • ...they (the nodes) have the same probability to be selected.

As above, change "to be selected" to "of being selected"

  • ...they (the nodes) have the same probability of being selected..."

But the same probabilty as what? You know it's the same probability as each other, but it's awkward/wordy to say "same probability as each other."

It would be clearer and more concise to say:

  • ...each node has the same probability of being selected..."

But this still doesn't say what the node will be selected for, because this sentence fails to mention the "destination node"! So we need to mention it, like so:

  • ...each node has the same probability of being selected as the destination node

Oops! now it's still ambiguous because there's a misleading "same.....as" structure, implying that the destination node is a separate node that has the "same" probability as the other nodes of being selected (for what, we know not!)

So, take out the "as", and we have:

  • ...each node has the same probability of being selected the destination node.

Personally, I like this last one best.

  • Awesome Answer, but I think you need to add of in the : there is an equal probability of any of the nodes being selected as the destination node. – Cardinal Oct 2 '15 at 9:27
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Sentences using "there is" are usable, so that you would say:

Due to the symmetrical positions, there is an equal possibility to select...

or

Due to the symmetrical positions, there is the same possibility to select...

But, expressions using "there is" could be round-about and/or wordy. Therefore, alternatively you could say:

Due to the symmetrical positions, the possibility is the same to select...

In addition, using "have" is also acceptable, I think.

  • Thank you. However, possibility and chance are not suitable in the context of mathematics. – Cardinal Aug 30 '15 at 22:57
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Just add "because they have X, " to the start of any of these.

They're all equal candidates.

They're all good candidates.

They all have their merits.

They're all a good choice.

All of them are a good fit.

It could be any of them.

Any would be a suitable choice.

They're equally suitable.

Any of them are sound.

Equal in their suitability.

Equally probable.

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Since you seem to want a technical term, I'd suggest

Due to the symmetrical positions, all nodes are equiprobable destination selections.

or

Due to the symmetrical positions, each node is equiprobable as a destination selection.

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Your third sentence sounds good, you may write also

Due to the symmetrical positions, they have the same chance to be selected as the destination node

..., their chance to be selected as the destination node is the same.

Or

..., the probability of selecting each of them as the destination node is equal.

..., they are of equal probability to be selected as the destination node.

  • Thank you, but chance is not preferable here. I've edited the question. – Cardinal Aug 30 '15 at 23:02
  • @Cardinal "they have the same chance" is more idiomatic than "have the same probability" and means the same, however if you note I also suggested sentences with probability – Ahmad Aug 31 '15 at 5:54

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