If you take two mutually independent events and somehow introduce a dependence between the two, then the events are no longer mutually independent and therefore by law of conditional probability, you can influence the probability of the outcome of the combination.
Corollary: If you take two mutually dependent events and somehow break the dependence between the two, then the events are no longer dependent and therefore by law of conditional probability and law of independent events, you can influence the probability of the outcome of the combination.
A practical example of the corollary would be password re-entry user interfaces during account registration.
The reason while re-entering the password the second time, we are not shown what we typed earlier is to make the reentry independent of the previous entry. Otherwise, we may look at what was typed earlier and subconsciously type the same thing -- which would be bad while we are doing account registration.
Corollary: If you take two mutually dependent events and somehow break the dependence between the two, then the events are no longer dependent and therefore by law of conditional probability and law of independent events, you can influence the probability of the outcome of the combination.
A practical example of the corollary would be password re-entry user interfaces during account registration.
The reason while re-entering the password the second time, we are not shown what we typed earlier is to make the reentry independent of the previous entry. Otherwise, we may look at what was typed earlier and subconsciously type the same thing -- which would be bad while we are doing account registration.