Can two events be both independent and mutually exclusive?

Can two events be both independent and mutually exclusive?

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.

Are independent events also mutually exclusive events?

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

Is it true that independence of two events A and B implies they are mutually exclusive?

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.

Can events be not mutually exclusive and not independent?

So mutual dependence is prerequisite for mutual exclusivity therefore mutually exclusive events can’t be independent.

What does it mean for two probabilities to be mutually exclusive provide an example of probabilities that are mutually exclusive?

By Paul King on January 17, 2018 in Probability. If two events are mutually exclusive, it means that they cannot occur at the same time. For example, the two possible outcomes of a coin flip are mutually exclusive; when you flip a coin, it cannot land both heads and tails simultaneously.

Can complementary events be mutually exclusive?

Complementary events are mutually exclusive. However, mutually exclusive events need not be complemen- tary. The fraction of the sample space which is in A is P(A).

Can 2 events be both independent and disjoint at the same time?

Two disjoint events can never be independent, except in the case that one of the events is null. Essentially these two concepts belong to two different dimensions and cannot be compared or equaled. Events are considered disjoint if they never occur at the same time.

How do you know if two 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 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.”

Can complementary events be independent?

Independence of complements: If A and B are independent, then so are A and B , A and B, and A and B . 4. Connection between independence and conditional probability: If the con- ditional probability P(A|B) is equal to the ordinary (“unconditional”) probability P(A), then A and B are independent.

What does it mean for two probabilities to be mutually exclusive?

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.

Are A and B mutually exclusive in probability?

Since P(B) > 0 and P(B|A) = 0, the requirement that an event be contained by A does affect the probability of B occurring, so A and B are not independent. Thus, if A and B are mutually exclusive, they are not independent.

How do you prove that two events are mutually exclusive?

Consider 2 events A and B which satisfy the condition that they both are mutually exclusive and independent (simultaneously). Thus, if we chose any 2 events such that at least one of them is guaranteed to not occur, then those two events will be both mutually exclusive and independent.

What is the probability of two events occurring at the same time?

The probability of both occurring at the same time is the product of the probability of each occurring: A way to get to equal is if either or equals . Then the events could be thought of as simultaneously independent and mutually exclusive. To do that let one or both of the events be impossible if that is permitted.

Independent Events: Two events A and B are independent if the probability of occurrence of one does not affect the probability of occurence of the other in any manner. Example: Getting a ‘6’ on roll of die and getting heads on toss of a coin are independent events. P (A & B) = P (A).