Final answer:
The statement is true; joint outcomes occur less often than their constituent outcomes because the joint occurrence cannot exceed the individual occurrences. Probabilities of joint outcomes are either zero, as in the case of mutually exclusive events, or the product of individual probabilities if the events are independent.
Step-by-step explanation:
The statement "Joint outcomes always occur less often (or as equally often in rare circumstances) than their constituent outcomes" is True. In the context of probability, a joint outcome refers to the occurrence of two or more events at the same time. For example, rolling a die and getting both a 1 and a 4 at the same time is impossible, hence a joint outcome in this scenario has a probability of zero. On the other hand, rolling a die and getting a 1 has a probability of 1/6, which is higher than zero. In cases where events are not mutually exclusive, the joint probability is still either less than or equal to the probabilities of the individual events occurring on their own because the joint occurrence cannot exceed the individual occurrences.
It's key to understand that when two or more events are mutually exclusive, their joint occurrence at the same time is impossible. However, when events are not mutually exclusive, their joint probability is the product of their individual probabilities, if they are independent, and is still less than or equal to the individual probabilities.One must also keep in mind that not all outcomes have the equal likelihood of occurring. For instance, a biased die may have a higher chance of landing on one number over another, which makes some outcomes more likely than others.