You get 4 times the same 10% chance, so the chance for failing with your attack on 4 cards is ~65.6% so about ~34.4% success chance for one attack.
edit: if you're interested on the calculation:
chance for success : c = 0.1
chance for fail : p = 1 - 0.1 = 0.9
number of cards : n = 4
calculation for chance to fail: p^n = 0.9 ^ 4 = ~0.656 = 65.6%
calculation for chance to succeed: 1 - (p^n) = 1 - 0.656 = 0.344 = 34.4%