What is an event with a probability of zero, if not an impossible event?

For a continuous random variable, such as a drop of water from a basin, the probability of a drop of water being taken is 1 n, and n tends to infinity, so the probability is zero.

Probability theory says that the probability of an impossible event is 0, but there is a 0 probability that an event can occur. For example, if you draw a person in the universe, you will be drawn. This is an example of how a 0-probability event can happen!

There are two types of random variables, continuous and discrete, and their respective distribution descriptions are different.

For continuous random variables, the probability density value of a single specific point is a bounded constant, which can be arbitrary (including 0 and 1), but because the point has no length, the probability density integral of the point is 0 (because the probability density value of the point is bounded), that is, the probability of the event corresponding to the point is 0, but the event is still possible because the event is in the event domain. That is, an event with a probability of 0 does not necessarily not necessarily not happen. Similarly, if the probability density value of a point is 1, the probability density integral of that point is still 0, so an event with a probability of 1 may not necessarily occur.

In summary, for continuous random variables, it makes no sense to discuss the probability of a single point (both are 0), we are talking about the probability that this random variable falls within an interval.

For a discrete random variable, if its event domain is a finite number of events, it can be assumed that an event with a probability of 0 will not occur, and an event with a probability of 1 will inevitably occur. But if the event is infinite, it needs to be analyzed in detail.

Since 0 probability events are all possible, then events with a probability close to zero are indeed possible, but when we usually deal with problems, we usually count events with a probability close to zero as 0 probability events, which are just counted, not absolute.

An event with a probability of zero is called zeroProbabilistic events, the impossible event is a zero probability event due to its zero probability, and the reverse is not necessarily.

For example, in the interval [0,1], the probability of randomly choosing a point to fall within [0,1 3] is 1 3, which is a classical geometric generalization. But for any 0, for a continuous random digging variable, the probability density of a single specific point.

The value is a bounded constant, which can be arbitrary (including 0 and 1), but because the point has no length, the probability density integral of the point is 0 (because the probability density value of the point is bounded), that is, the probability of the event corresponding to the point is 0, but the event is still possible because the event is in the event domain. That is, an event with a probability of 0 does not necessarily not necessarily not happen.

Probability is a numerical measure of the likelihood of a chance event occurring. Suppose after many repeated experiments (represented by x) and several times by chance (represented by a) occur several times (represented by y). Use x as the denominator.

y as a molecule, forming a numerical value (p is used to represent the focal beam). In multiple experiments, p is relatively stable at a certain value, and p is called the probability of a occurrence. The probability of a chance event is determined by long-term observation or a large number of repeated experiments, and this probability is statistical probability or empirical probability.

The discipline that studies the internal laws that govern accidental events is called probability theory.

It belongs to a branch of mathematics. Probability theory reveals the manifestations of the internal laws contained in accidental phenomena. So, probability, for people to know natural phenomena.

and social phenomena play an important role. For example, the amount of social goods that need to be deducted before they are distributed to individual consumption, and the proportion of accumulation that should be accounted for in national income need to be determined using probability theory.

The probability of an impossible event is 0, and this sentence is true.

Impossible Events: Probability Theory.

Events that are impossible to occur under certain conditions are called impossible events. People usually use 0 to indicate the likelihood of an unlikely event occurring. That is, the probability of an unlikely event is 0. However, an event with a probability of 0 is not necessarily an impossible event.

Impossible event definition.

Impossible events are random events.

One of the special cases refers to an event that must not occur in each trial under the same conditions, for example, if a dice rolls a 7, the frequency of the impossible event is always equal to zero, so the probability of the impossible event is equal to zero.

Inevitable event. Inevitable event, under certain conditions when repeated trial field test, some events will inevitably occur in each test, such an event is called an inevitable event, referred to as an inevitable event.

Continuous random variables.

x, the value is 0 for the probability of any finite number of points in the sample space, and the finite number of points is eliminated from the entire sample space'It should not be a finite number of points'The probability remains at 1.

Right. Impossible events: In probability theory, events that may occur without regret under certain conditions are called impossible events.

People usually use 0 to indicate the likelihood of an unlikely event occurring. That is, the probability of an unlikely event is 0.

However, an event with a probability of 0 is not necessarily an impossible event.

It is impossible for the event to be determined.

The impossible event is one of the special cases of random events, which refers to the event that must not occur in each trial under the same conditions, for example, if a dice rolls a 7, the frequency of the impossible event is always equal to zero, so the probability of the impossible event is equal to zero.

Inevitable event. Inevitable event, when the test is repeated under certain conditions, some events will inevitably occur in each test, such an event is called an inevitable event, referred to as an inevitable event.

The continuous random variable x, whose value is 0 probability of any finite number of points in the sample space, is obtained by eliminating this finite number of points from the entire sample space'It should not be a finite number of points'The probability remains at 1.