In my Interlinear bible, the words 'ye may be healed' come under one Greek word iaomai (Strongs No G2390) to cure, heal, make whole. For some, adding the word may introduces some doubt, ie may or may not be healed. Why did the translators add these words to to this verse and not to any others were the word healed is used.
This is a simple grammatical question that is resolved by understanding how the Greek works.
Greek is a highly inflected language, especially the verbs. The verb in question here is: ἰάομαι (iaomai) = "I heal", in its lexical form; however, in James 5:16 it occurs in the form ἰαθῆτε (iathēte) = Verb - Aorist Subjunctive Passive - 2nd Person Plural; and so must be translated, "you [plural] may be healed".
Because of the versatility and inflection in the Greek verbs, pronouns are only rarely needed because the verb contains all that is required to convey the meaning. This is a perfect example where the pronouns have not been used but the sense is perfectly clear.
Lastly, note that the "mood" of the verb is "subjunctive" and the "voice" is "passive", that is why it must be translated with a "may" and that the action is not done by the subject.
Your translation is quite valid and every other version will show something similar.
Strongs No G2390 iaomai shows the lexicon (dictionary) spelling and meaning of a Greek word. When this word is used in James 5:16, it is spelled as iathēte. That is its subjunctive form. The Greek subjunctive mood primarily refers to HYPOTHETICAL actions in the PRESENT or FUTURE. In English we use the subjunctive mainly when talking about events that are not certain to happen.
Further, hopōs iathēte (so that you may be healed) forms potential subjunctive purpose clause. It is not 100% definite but it has that potential. The focus is on the positive potential.
That is why it is translated as 'may be healed' in James 5:16. The translators translate the lexicon meaning of the word plus its subjunctive mood.
In https://biblehub.com/james/5-16.htm, 25 out of 27 versions translated as 'may be healed'. It is the overwhelming consensus. Good News Translation has over-translated iathēte
So then, confess your sins to one another and pray for one another, so that you will be healed. The prayer of a good person has a powerful effect.
Because this seems to have been the standard way of formulating expressions of this type in early modern English. The presence of the conjunction that modifies the auxiliary verb usually responsible for constructing the future tense, resulting in an(other) tense altogether, called conjunctive or subjunctive. (For more information, feel free to consult our two sister sites, Linguistics.SE and English.SE). Thus, within the traditional King James version, the statistical distribution is as follows:
- that you/ye may appears 92 times,
- that you/ye might appears 27 times,
- that you/ye be appears eleven times,
- that you/ye will appears seven times.
Similarly for other pronouns:
- that I may appears 144 times,
- that I will appears 66 times,
- that I might appears 39 times,
- that I be appears twice.
- that (s)he may appears 103 times,
- that (s)he might appears 69 times,
- that (s)he will appears twenty times,
- that (s)he be appears twice.
- that we may appears 74 times,
- that we might appears nineteen times,
- that we will appears six times,
- that we be appears twice.
- that they may appears 155 times,
- that they might appears 66 times,
- that they be appears ten times,
- that they will appears five times.
It follows that, by and large, the most frequent auxiliary verbs, in descending order of preference, are:
- may, appearing (over) 568 times,
- might, appearing (over) 220 times,
- will, appearing (over) 104 times,
- be, appearing (over) 27 times.
(The above is for pronouns only; other auxiliaries are shall, shalt, and should, for which the interested reader is invited to construct their own tables, using a biblical software of their own choice; personally, I have employed Theophilos).