Peace be upon you, We usually use the sentence you mentioned as it is in the following form: you've get the wrong answer. That is beacause that numberis talked about is already known for the speaker and the hearer, so it is defined. Usually 'the' is used before nouns that the speaker and the hearer know about.
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norwolfYou’ve got a/the wrong number.the wrong is the combination you want. You can almost think of the two as a fixed pattern. the wrong.
tranquilityWhat follows is the correction of 'you've get the wrong answer': you've got the wrong number.You asked about 'the wrong number' not 'the wrong answer', right?
CalifJimnorwolfYou’ve got a/the wrong number.the wrong is the combination you want. You can almost think of the two as a fixed pattern. the wrong.The police arrested the wrong man. They've got the wrong man.I dialed the wrong number. I went to the wrong address.You don't understand my true motives. You've got the wrong idea about
khoffWhether or not I think the caller realizes his mistake has nothing to do with the choice of articleVery true. I agree.
norwolfI copied the sentence from a grammar book. It allows the two articles alternative.Theoretically, you can use a wrong, particularly in hypotheticals in subordinate clauses, but the wrong is almost always what you want. Note that in these cases you are usually speaking in generalities. Example: