Final answer:
Two events cannot be mutually exclusive and independent simultaneously.
Step-by-step explanation:
Two events cannot be mutually exclusive and independent simultaneously.
Mutually exclusive events are events that cannot occur at the same time and have no overlapping outcomes. For example, if event A is flipping heads on a coin and event B is flipping tails, these events are mutually exclusive because both cannot happen at the same time.
On the other hand, independent events are events where the occurrence of one event does not affect the probability of the other event happening. For example, if event A is rolling a 4 on a fair die and event B is flipping heads on a fair coin, these events are independent because rolling a 4 does not impact the likelihood of flipping heads.
Since mutually exclusive events have no overlapping outcomes, there cannot be a scenario where they are independent.