I am almost certain there is some magical statistical way to figure this out, but although I have some knowledge of stats, I don't have that much. I do however have enough knowledge to write a simple script to generate a LOT of random numbers. So that is what I did.
The script rolled each die 100,000 times and assigned success based on a roll of 6+ on either die.
==========D6==============
d6 & d0
Success Rate: 16%
d6 & d6
Success Rate: 30%
d6 & d8
Success Rate: 47%
d6 & d10
Success Rate: 58%
d6 & d12
Success Rate: 65%
==========D8==============
d8 & d0
Success Rate: 37%
d8 & d6
Success Rate: 47%
d8 & d8
Success Rate: 61%
d8 & d10
Success Rate: 68%
d8 & d12
Success Rate: 73%
==========D10==============
d10 & d0
Success Rate: 49%
d10 & d6
Success Rate: 58%
d10 & d8
Success Rate: 68%
d10 & d10
Success Rate: 75%
d10 & d12
Success Rate: 79%
==========D12==============
d12 & d0
Success Rate: 57%
d12 & d6
Success Rate: 65%
d12 & d8
Success Rate: 73%
d12 & d10
Success Rate: 79%
d12 & d12
Success Rate: 82%
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