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When two events are disjoint they are also independent?
When two events are disjoint (or mutually exclusive), it means that they cannot occur at the same time; if one event occurs, the other cannot. Consequently, disjoint events cannot be independent, because the occurrence of one event affects the probability of the other event occurring. In fact, for disjoint events, the probability of both events happening simultaneously is zero, which contradicts the definition of independence where the occurrence of one event does not influence the other. Therefore, disjoint events are not independent.
If A and B occur cannot at the same time. Are they called mutually exclusive?
Yes, if events A and B cannot occur at the same time, they are called mutually exclusive. This means that the occurrence of one event excludes the possibility of the other event happening simultaneously. In probability terms, the probability of both A and B occurring together is zero.
Can two events be mutually exclusive and independent simultaneously?
No, two events cannot be mutually exclusive and independent simultaneously. Mutually exclusive events cannot occur at the same time, meaning the occurrence of one event excludes the possibility of the other. In contrast, independent events are defined such that the occurrence of one event does not affect the probability of the other occurring. Therefore, if two events are mutually exclusive, the occurrence of one event implies that the other cannot occur, which contradicts the definition of independence.
Does spinning a four section spinner affect a six-sided number cube will land upon when tossed?
Presuming that the spinner and the number cube are both "fair", then no - spinning the spinner and tossing the six-sided number cube are called statistically independent events. They do not influence each other, and it does not matter which order the events occur in.
If the probability of two events occurring together is 0 the events are called?
If the probability of two events occurring together is 0, the events are called mutually exclusive. This means that the occurrence of one event precludes the occurrence of the other, so they cannot happen at the same time. For example, flipping a coin can result in either heads or tails, but not both simultaneously.
When two events are disjoint they are also independent?
When two events are disjoint (or mutually exclusive), it means that they cannot occur at the same time; if one event occurs, the other cannot. Consequently, disjoint events cannot be independent, because the occurrence of one event affects the probability of the other event occurring. In fact, for disjoint events, the probability of both events happening simultaneously is zero, which contradicts the definition of independence where the occurrence of one event does not influence the other. Therefore, disjoint events are not independent.
Event A has probability 0.4 event B has probability 0.5 If A and B are disjoint then the probability that both events occur is?
If two events are disjoint, they cannot occur at the same time. For example, if you flip a coin, you cannot get heads AND tails. Since A and B are disjoint, P(A and B) = 0 If A and B were independent, then P(A and B) = 0.4*0.5=0.2. For example, the chances you throw a dice and it lands on 1 AND the chances you flip a coin and it land on heads. These events are independent...the outcome of one event does not affect the outcome of the other.
Can two disjoint sets be equivalent?
Yes,Because not all disjoint no equivalent other have disjoint and equivalent
Are complementary events also mutually exclusive events?
Yes, they are. Mutually exclusive events cannot occur together. Complementary events cannot occur together either because an event and its complement are the negative of each other.
What dies it mean for events to occur independently?
When events are to occur independently, that means all of the events will happen on their own with no form of trigger from another. They are all independent of each other and will happen when they decide to happen.
Difference betweenDisjoint sets and pairwise disjoint sets?
Assuming that, by 'disjoint', you mean that a collection of sets has an empty intersection, here is the difference between pairwise disjoint and 'disjoint': If a collection of sets is pairwise disjoint, it implies that the collection is 'disjoint': If no two sets overlap, then no k sets would overlap for any k, since this would require the overlap of at least two sets i.e. you know for sure that k things aren't in contact at a common point if you know that no two of them are in contact with each other. However, if a collection of sets is 'disjoint' (so the overall intersection is empty), it doesn't mean that the collection is pairwise disjoint. For instance, you could have a collection of 4 sets containing two overlapping pairs, where no set in one pair overlaps with a set in the other. So the intersection of the whole thing would be empty without pairwise disjointness. You could have a few things in contact with each other without all of them sharing a point of contact.
What is a joint sets and disjoint sets?
Joint sets:Joint sets are those which have common elements Disjoint sets : A pair of sets is said to be disjoint if their intersection is the empty set. That is to say, if they share no elements. All of the usual operations can be performed on disjoint sets, so long as the operation makes sense. (For example, taking the complement of one with respect to the other could pose problems.)
What events are correlated but do not necessarily have causal relationship?
You did not list any events.
What is it called when two events in which one of the other can happen but they can not happen at the same time?
When two events cannot occur simultaneously but one may happen if the other does not, they are referred to as "mutually exclusive events." In probability theory, this means that the occurrence of one event precludes the occurrence of the other. For example, when flipping a coin, the outcomes of heads and tails are mutually exclusive.
What are the major events that may occur in the lives of older people?
Some of the major events that may occur in the lives of older people include witnessing marriages of their children or births of grandchildren. Other major events may include marking anniversaries.
What natural events can occur when crustal plates move over each other?
earthquakes and tsunamis
What events occur to build mountain range?
Most mountain ranges occur in the region of major plates colliding with each other, forcing one to go over top of the other.
