Step 1: Recall what a binomial experiment requires.
A binomial distribution rests on a few fixed conditions, and the odd-one-out among the options is the false one.
Step 2: Condition one, fixed identical trials.
There must be a fixed number $n$ of identical trials. So option (1) is a true property.
Step 3: Condition two, two outcomes.
Each trial has only two outcomes, success or failure. So option (2) is a true property.
Step 4: Condition three, constant probability.
The probability of success must stay the same from trial to trial. Option (3) claims the probabilities can change, which violates this rule.
Step 5: Condition four, independence.
The trials must be independent. So option (4) is a true property.
Step 6: Pick the wrong statement.
The only statement that is not a property is option (3).
\[ \boxed{\text{The probabilities of the two outcomes can change from one trial to the next}} \]