Can events be exhaustive and independent?
An infinite set of events, however, can be both independent and exhaustive. The set is said to be mutually independent (or simply in- dependent) if it is k x k independent for all k. There are numerous examples in the literature (Parzen 1960, p. 90; Feller 1968, p.
Can two events be mutually exclusive and independent simultaneously?
Can two events be mutually exclusive and independent simultaneously? “Table events can be mutually exclusive and independent simultaneously”. Two independent events are always mutually exclusive.
Can an event be mutually exclusive and exhaustive at the same time?
When two events are mutually exclusive, it means they cannot both occur at the same time. When two events are exhaustive, it means that one of them must occur. Think again of a coin toss. The results are mutually exclusive (it will be either heads or tails; it can’t be both on the same flip).
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.
What does it mean when two events are exhaustive?
In probability, a set of events is collectively exhaustive if they cover all of the probability space: i.e., the probability of any one of them happening is 100\%. If a set of statements is collectively exhaustive we know at least one of them is true.
What is the difference between events that are dependent and events that are independent?
Dependent events influence the probability of other events – or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.
When two consecutive events occur each one with its own probability that does not depend on the the probability of the other event we say that the two events are?
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll.
Can two complementary events occur at the same time?
Complementary events are mutually exclusive events since they cannot occur at the same time. They are also considered as exhaustive events since the sum of their probabilities must be 1.
What are mutually exclusive and equally likely events give two examples for each?
Germination and non germination are mutually exclusive events. Outcomes of a trial are said to be equally likely if taking in to consideration all the relevant evidences, there is no reason to expect one in preference to the others.
Is mutually exclusive the same as 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.
When two events are independent the probability of both occurring is?
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events. where P(A and B) is the probability of events A and B both occurring, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.
How do you know if two events 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.