Explanation:

When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event happening. In other words, the probability of event A occurring is not influenced by the occurrence or non-occurrence of event B, and vice versa.

Mutually Exclusive:
When two events are mutually exclusive, it means that they cannot occur at the same time. If event A happens, event B cannot happen, and vice versa. For example, if you toss a coin, the outcomes of getting a head and getting a tail are mutually exclusive.

Independence and Mutually Exclusive:
If two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event happening. However, if events A and B are mutually exclusive, it means that they cannot occur at the same time. These two concepts are contradictory.

Example:
Let's consider an example to understand this concept better. Suppose event A represents the outcome of rolling a fair die and event B represents the outcome of flipping a fair coin. Both event A and event B are independent because rolling a die does not affect the outcome of flipping a coin, and flipping a coin does not affect the outcome of rolling a die.

Now, let's say that event A is defined as rolling an even number (2, 4, or 6) on the die, and event B is defined as flipping a head on the coin. These events are not mutually exclusive because it is possible to roll an even number on the die and also flip a head on the coin.

Conclusion:
Therefore, if two events A and B are independent, they cannot be mutually exclusive. The occurrence of one event does not affect the probability of the other event happening, so they can both happen simultaneously.