The following example is as follows:
You have 10 coins divided into 2 groups (A and B), each coin has a different chance to roll heads or tails depending on the coin it is rolled against. To make it clear: Each time a coin from group A is rolled, a coin from group B is simultaneously rolled as well. The coin from group A has a different chance to roll heads or tails given which coin it is rolled against.
Below is a an example table matrix of Coins 1-5 and their chances of rolling Heads in every possible circumstance (rolling against coins 6-10)
That is to say, c1c6 is the probability of coin 1 in group A to roll heads when rolled with coin 6 simultaneously and is 31%. Something to note: this is symmetrically opposite to the coin 6 roll, meaning coin 6 has a 69% chance to roll heads in this scenario.
The question is: What is the probability of coins 1-5 to all roll heads, when ALL coins 1-10 are rolled simultaneously?