I am enrolled in an Oxbridge computer science graduate program. We are required to pass our top 6 modules, which I did. I actually did really well in some modules. However, I decided to register for a 7th exam that I did not attend the lectures for, under the impression that I can always delete the grade from my record (someone told me that). The exam turned out to be very difficult and I failed. It turns out I cannot delete the grade from my record. What is the best way to mitigate this situation given that I was aiming for competitive phd programs in the US?
My dissertation went extremely well and I will have 3 glowing LORs and I got distinctions in all other theoretical courses, some of which are considered really difficult. If I explain in my phd application that I took the exam for fun, would this make the phd committee disregard the failing grade?