Can mutually exclusive events be independent?
Suppose two events have a non-zero chance of occurring. Then if the two events are mutually exclusive, they can not be independent. If two events are independent, they cannot be mutually exclusive.
What are mutually exclusive events vs independent?
Two events are mutually exclusive when they cannot occur at the same time. For example, if we flip a coin it can only show a head OR a tail, not both. Independent event: The occurrence of one event does not affect the occurrence of the others.
Can two events be mutually exclusive as well as mutually independent explain?
No. Mutually exclusive means they can’t both occur—if one occurs, the other definitely does not. So, if A and B are mutually exclusive, then P(A|B) = 0. If events are independent, it means that learning about one gives you no information about the other, so P(A|B) = P(A).
What does independent mean in probability?
Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)
What does mutually independent mean?
A finite set of events is mutually independent if every event is independent of any intersection of the other events. —that is, if and only if for every and for every k indices , (Eq.3) This is called the multiplication rule for independent events.
What is independent event?
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Can two probabilities be mutually exclusive and also independent?
All Answers (7) If two events are mutually exclusive then they do not occur simultaneously, hence they are not independent.
How do you know if probabilities are independent?
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
What are mutually independent events?
How do you determine independence?