Typically, Events can be termed as exclusive if the occurrence of one event does not depend on the existence of another event. In addition to that, mutually exclusive events cannot take place at the same duration. For instance; in an election, the outcome is either a win (A) or a lose (B), and the events are not dependent.

Probability of (A) + Probability of (B) = 1 (Probability space)

A-B = 0

However, events can be termed as independent if the appearance of a specific event does not depend or is not influenced by the appearance or occurrence of another event. For example, when tossing two different coins the outcome of one coin is not necessarily dependent on the outcome of the other coin.  Therefore, flipping one coin is entirely not dependent on the outcome of the other coin being flipped.

The probability of an event (A) and Probability of event (B) = P (AB)

The possibility of occurrence (A) + Probability of event (B) is not equal to one.

This is a clear indication that mutually exclusive events cannot be independent. At the same time, independent events can never be mutually exclusive. This is mostly because events with a measure of zero can also be accommodated.

P (A and B) is true when P is equal to (AB) since the events are completely independent. However, the equation is false if the events are mutually exclusive since

Probability of (A) + Probability of (B) = 1 (Probability space)

P (A and B)= P (A+B)= 1

The probability of A and B equaling to the probability of (A+B) is true when the events are mutually exclusive. However, when the events are independent, then the equation is not true because for independent events the equation is

The probability of an event (A) and Probability of event (B) = P (AB)

The probability of an event (A) + Probability of event (B) is not equal to one.