Seems that probability of AC is (1/10) ^ k where k is number of tests.
So probability to get just one AC after N attempts is 1 - ( 1 - (1/10) ^ k ) ^ N
^_^
Good luck. ;)

P.S.: if k = 10, you have to make 6931471806 attempts for making this probability greater then 0.5 xD
P.P.S: ...if i made no mistakes. ;)