Can an event be independent but not mutually exclusive?
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.
Is independent events mutually exclusive?
An example of a mutually exclusive event is when a coin is a tossed and there are two events that can occur, either it will be a head or a tail. Hence, both the events here are mutually exclusive….
| Difference between Mutually exclusive and independent events | |
|---|---|
| Mutually exclusive events | Independent events |
Can two events be both independent and mutually exclusive Why or why not?
Originally Answered: Can 2 events be mutually exclusive and independent? Not unless one of them has probability zero. Therefore P(A) = 0 or P(B) = 0. If at least one of the events has zero probability, then the two events can be mutually exclusive and indepenent simultaneously.
What does it mean when events are not mutually exclusive?
Mutually exclusive events are events that can not happen at the same time. Examples include: right and left hand turns, even and odd numbers on a die, winning and losing a game, or running and walking. Non-mutually exclusive events are events that can happen at the same time.
What is an independent event in probability?
In probability, we say two events are independent if knowing one event occurred doesn’t change the probability of the other event. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn’t change the probability of getting “heads.”
What is the difference between mutually exclusive and independent events in probability?
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.
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.
Are events independent or dependent?
In general, an event is deemed dependent if it provides information about another event. An event is deemed independent if it offers no information about other events.
What is a mutually exclusive event in probability?
If two events have no elements in common (Their intersection is the empty set.), the events are called mutually exclusive. Thus, P(A∩B)=0 . This means that the probability of event A and event B happening is zero. They cannot both happen.
How do you know if an event is independent?
How do you know if probabilities are 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.
What are independent events probability?
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.