Question

“If two events are mutually exclusive, they must not be independent events.” Is this statement true or false? Explain your choice.

Answer 1

Answer:

its True.

Events are mutually exclusive if the occurrence of 1 event excludes the occurrence of the other(s). Mutually exclusive events cannot happen at an equivalent time. For example: when tossing a coin, the result can either be heads or tails but can't be both.

P(A∩B) = 0

P(A∪B) = P(A)+P(B) mutually exclusive A, B

P(A∣B) = 0

P(A∣¬B) =P(A) / 1−P(B)

Events are independent if the occurrence of 1 event doesn't influence (and isn't influenced by) the occurrence of the other(s). For example: when tossing two coins, the results of one flip doesn't affect the results of the opposite .

P(A∩B) = P(A)P(B)

P(A∪B) = P(A)+P(B)−P(A)P(B)

P(A∣¬B)=P(A) independent A,B

This in fact means mutually exclusive events aren't independent, and independent events can't be mutually exclusive. (Events of measure zero excepted.)