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# what is basic difference between mutually exclusive event & independent event?

Rahul Kumar
131 Points
9 years ago

mutually exclusive events cant occur at the same time, such as rolling 6 with one die and rolling three on the sdame die.

independent events have the same probability of occurring regardless of the outcome of the other, rolling six on a red die, and rolling 5 on a blue die (rolling both dice together) are independent.

Kolla Raja Sekhar
51 Points
9 years ago

Maybe itll be clearer if you look at the definitions in terms of probabilities.

Im guessing youve been taught that the probabilities of independent events arent affected by each other, and that mutually exclusive events cant happen at the same time.

More mathematical ways of saying those things are:

Independent: - P(A and B) = P(A)xP(B)
Mutually exclusive: - P(A and B) = 0, where A and B are two events.

Comparing those two definitions, its clear that theyre different. In fact, events cant be independent and mutually exclusive at the same time.

This is fairly clear if you think about it: If event A happens then event B cant happen, and thus event B is dependent on event A (and vice versa).

The exception to this is when one of your events is impossible, such as rolling a 7 on a dice.