CAN A and B be both mutually exclusive and 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.

Can a mutually exclusive events be independent?

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 prove that events A and B 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.

Can two events A and B be independent of one another and disjoint explain what conditions are needed for this to happen?

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.

When two events A and B are independent the probability of their intersection can be found by multiplying their probabilities?

joint probability
The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B. c. When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events.

How do you show that three events are independent?

Three events A, B, and C are independent if all of the following conditions hold P(A∩B)=P(A)P(B), P(A∩C)=P(A)P(C), P(B∩C)=P(B)P(C), P(A∩B∩C)=P(A)P(B)P(C).

Which statement implies that A and B are independent events?

Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B) = P(B ∩ A) = P(B) × P(A).

Can two events A and B be independent of one another and disjoint?

A and B Not Disjoint If events are disjoint then they must be not independent, i.e. they must be dependent events.

When events A and B are said to be independent What does that mean?

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

When A and B are mutually exclusive events?

A and B are mutually exclusive events if they cannot occur at the same time. Said another way, If A occurred then B cannot occur and vise-a-versa. This means that A and B do not share any outcomes and P (A ∩ B) = 0.

How do you know if a probability distribution is mutually exclusive?

Certain things can be determined from the joint probability distribution. Mutually exclusive events will have a probability of zero. All inclusive events will have a zero opposite the intersection. All inclusive means that there is nothing outside of those two events: P(A or B) = 1.

What does p(b|a) mean?

Note that P (B|A) is the conditional probability of event B occurring, given event A occurs. The following examples show how to use these formulas in practice.

How do you find the probability of two events being independent?

If events are independent, then the probability of them both occurring is the product of the probabilities of each occurring. P (A) = 0.20, P (B) = 0.70, A and B are independent. The 0.14 is because the probability of A and B is the probability of A times the probability of B or 0.20 * 0.70 = 0.14.