There should be a provision to delete answers to your questions if you think that it could decrease the chances of getting your question answered. For example, While going through questions, I tend to ignore the ones which have 1 or more answers. The higher the number, the more I tend to not go for them (answering them). So would it not be a good idea to provide the original poster with the facility to delete answers to their questions?
The correct response to answers that don't actually answer your question is to down-vote them. If the answer gets down-votes the poster will (hopefully) either improve it to correct the mistakes or delete it. Both of which solve your problem.
Allowing the OP to delete answers "they don't like" would lead to abuse.
SO's questions and answers aren't meant to help only the person who posted the question, but all future visitors that have the same problem. That's also why we close questions as too localized.
A question poster deleting an answer because he doesn't like it stomps all over that...
Answers should not be deleted because you don't like them; this is true for everybody.
There is already a process used to delete an answer, and that involves at least three users who can vote to delete an answer with a negative score.
Leaving the decision of deleting answers to the user who asked the question is the last thing I would see implemented, also because there are users who, instead of accepting the fact they didn't expose the problem in the correct way, they would say the answer is wrong. It is probable that another user would be more objective about the given answers.
About the chances of getting the question answered, that is purely subjective, and you cannot be sure the question will never be answered, even if there is already an answer. There are two cases:
- The answer is utterly wrong, or it's not the best answer
- The answer is a very good one
In the first case, it is probable a user will answer the question to show that the previous answer is utterly wrong, or suggesting something that it is preferable not doing; in the second case, there should be a user who offers an alternative solution.
In the first case, a new (possibly better) solution is given; in the second case, you already had a very good solution, but you get an alternative solution.
I would say that the chances of getting an answer depends from the question, not from the existing answers, which would eventually be an incentive for giving an alternative solution.
If the question is interesting, or shows efforts in finding a solution, it is probable that more users will try answering it. If the question is asking something too localized, for which the OP is the only one interested in the answer, then it is probable few users will try answering it.