Final answer:
Events A and B are mutually exclusive if they cannot occur at the same time, meaning P(A∩B) = 0 is true. This is because mutually exclusive events do not have any outcomes in common. An example showing mutually exclusive events is when two different numbers are rolled on a die.
Step-by-step explanation:
The statement is true: events A and B are mutually exclusive if P(A∩B) = 0. This implies that the two events cannot happen at the same time, which is the definition of being mutually exclusive. To illustrate this concept with an example, imagine rolling a die. The events of rolling a '1' (Event A) and rolling a '6' (Event B) are mutually exclusive because you cannot roll a '1' and a '6' at the same time, hence P(A ∩ B) would indeed be equal to 0.
However, if we look at Event A as rolling an odd number and Event B as rolling an even number, then these two events are also mutually exclusive. This is because the outcomes are distinct with no overlap, therefore, the probability of both occurring simultaneously, P(A ∩ B), is 0.