Re-apply to slightly different position after 3 months. Yay or nay?

I applied to a position in this company a bit over 3 months ago. I got a first phone interview and they seemed very interested. However I then was asked to do a programming test and I scored only 68% on it due to misunderstanding the third task (1st and 2nd went well). They let me know that my results were 'not convincing'.

Well.. I hate my current job so ya.. that same company now has another open position that is slightly different but still applicable for me, but it's only been 3 months so I don't know if I should even try. Plus it's the same recruiter taking care of it.

Do I even have a chance? And if I do decide to try, should I mention the last attempt in my cover letter?

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