What is the difference between 是不是吃了蛋糕？ and 吃蛋糕了没有？
是不是喝酒了? and 喝酒了没有？
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The first expression is usually used when the speaker has a feeling that the other person had done something, so he's making a guess, while the second could be either a simple question or suggestion.
In the first case,
can be used when the speaker noticed a cream stain on the other person's shirt or something like that. The speaker is guessing if the other person has had a cake.
can be used when the speaker wants to suggest the other person to have a nice piece of cake or simply query whether he has had cake.
Your wife asks "你是不是到外面泡妞啦". Your brothers ask "你到外面泡妞了没有".
In case you missed the point: "你是不是到外面泡妞啦" means your wife does not know whether you were flirting with other women, but she strongly thinks you were. This is because most women in love are paranoia. "你到外面泡妞了没有", on the other hand, is a neutral question without any guesses. Your brothers ask in this way because they trust you.
“是不是吃了蛋糕？” This sentence's emphasis is on whether or not the person ate cake.
“吃蛋糕了没有？” This sentence's emphasis is on whether the person ate cake or something else.
Generally speaking, the two sentences have fundamentally the same meaning. In real life, the result is the same.
你是不是吃蛋糕了? This is as though the asker is suer you have eaten, but still asks you.
吃蛋糕没有？This is asking if you have eaten the cake or not.
Regardless of this, the asker still gets the same answer.
General if you drink and someone can smell it you will be asked "Have you been drinking?". If there is no smell someone might ask: "Have you had a drink?".
You don't know he has a cake or not, but you are guessing, then you use the first one.
You know that he has a cake, you just want to make sure did he eat it or not, then you use the second one.
Both of them are asking yes or not, but the first one is asking about the thing, is it a cake or a biscuit? The second one is asking about the action, have you eaten it or not?