Final answer:
The term for when two conditions cannot occur together is 'mutually exclusive.' Events A and C would be mutually exclusive if P(A AND C) = 0. Statistical tests may be used to determine if such exclusivity or independence exists between other events.
Step-by-step explanation:
The term you're looking for when two conditions cannot occur together is known as mutually exclusive. If events A and C don't share any outcomes in common, as stated by the condition P(A AND C) = 0, then we can say that A and C are indeed mutually exclusive.
Likewise, if it is not clear whether events A and B are mutually exclusive, you should not presume they are until it's proven. An example of mutually exclusive events would be the scenario where you cannot draw a playing card that is both a heart and a club at the same time.
Therefore, the events 'drawing a heart' and 'drawing a club' are mutually exclusive, since P(A AND B) = 0. To determine if events D and E are independent or mutually exclusive, statistical tests can be used that examine the probabilities of each event occurring both separately and together.