Can something be mutually exclusive and statistically independent?
Yes, there is relationship between mutually exclusive events and independent events. Thus, if event A and event B are mutually exclusive, they are actually inextricably DEPENDENT on each other because event A’s existence reduces Event B’s probability to zero and vice-versa.
What is a mutually exclusive event in statistics?
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.
Are mutually inclusive events independent or dependent?
Another way to think of it is that two mutually inclusive events cannot happen independently. If you have two events that are dependent in some way, they are mutually inclusive. In probability terms, two events are mutually inclusive if their intersection is greater than zero: P(A or B) > 0.
How do you know if two events are mutually exclusive?
Two events are mutually exclusive if they cannot occur at the same time. If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
Can two events be both mutually exclusive and independent at the same time?
However the event that you get two heads is mutually exclusive to the event that you get two tails. 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.
How do you know if A and B is mutually exclusive?
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0. If it is not known whether A and B are mutually exclusive, assume they are not until you can show otherwise.
What does independent mean in statistics?
Two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other (equivalently, does not affect the odds).
What is mutually inclusive and mutually exclusive?
2 events are mutually exclusive when they cannot both occur simultaneously. Mutually inclusive events. 2 events are mutually inclusive when they can both occur simultaneously.
What are independent events in statistics?
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)
How do you know if its mutually exclusive or independent?
The difference between mutually exclusive and independent events is: a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time whereas independent event occurs when one event remains unaffected by the occurrence of the other event.
What is independent in statistics?
An independent event is an event that has no connection to another event’s chances of happening (or not happening). In other words, the event has no effect on the probability of another event occurring. When two events are independent, one event does not influence the probability of another event.