How to treat embedded questions and が

Question

What is the difference between following sentences?

できるかどうか分かりません
できるかどうかが分かりません

Both seem to have about similar amount of hits on google for an exact phrase.

When reading about embedded sentences they don't tend to mention が to follow them, so it's probably not が would be grammatically required. If that is so, what is its function?

This mentions that を can be used, but no mention of が

This asks about と, which seems to make it a quote, but don't know if it necessarily changes the meaning

This post seems close but the answer bottom makes it seem like が is required by the nature of 分かる while other sources teach it without it.

Answer 1

The が here emphasises what comes before it. You could imagine it as a response to a question:

Speaker A: 何かが分かりませんか。

"Is there something that you don't understand?"

Speaker B: できるかどうかが分かりません。

"I don't understand whether I can do it or not."

It emphasises that Speaker B is unsure about that specific thing, the important part of the sentence being not that Speaker B is unsure of something/anything, but that Speaker B is specifically unsure of whether or not he/she can do it.

Answer 2

In our daily conversation, we tend to omit が and を. For example, we write ケーキを食べますか？ but we say ケーキ食べますか？

It is the same for できるかどうか分かりません and できるかどうかが分かりません. The former is casual and the latter is for former writing.

を is used because of 知らない. Please memorize を+知らない and が+分かります. This is standard grammar.

For these sentences 雨がいつ降るかと大変楽しみにしていましたが、なかなか雨が降りません。and 雨が降ることを大変楽しみにしていましたが、なかなか雨が降りません。The former gives me a feeling that the person is looking forward to the rain more. As another user has mentioned- more excited to the rain.