# Down arrow? Probability question

• Office_Shredder
In summary, the "Down arrow" in probability is a symbol used to represent conditional probability, indicating the likelihood of an event occurring given that another event has already occurred. It is used in probability calculations to show the relationship between two events, where the probability of one event is dependent on the occurrence of another event. It can also be used in other areas of science, such as in physics and chemistry. The difference between the "Down arrow" and the "Up arrow" is that the former represents conditional probability, while the latter represents the inverse of conditional probability. To remember the meaning of the "Down arrow", think of it as a downward flow of information, where the probability of the second event is affected by the first event.
Office_Shredder
Staff Emeritus
Gold Member
A question on my probability problem set reads: If the sequence of events An is non-decreasing (i.e. An is a superset of An+1 for all n), prove the following

$$P[A_n] \downarrow P[\bigcap_{i=0}^\infty A_i]$$

I just need to know what the heck the down arrow means

I think it means that the probabilities on the left are a non-increasing sequence converging to the number on the right (that's what you have to prove).

## 1. What is the meaning of the "Down arrow" in probability?

The "Down arrow" in probability refers to the symbol used to represent conditional probability, which is the likelihood of an event occurring given that another event has already occurred.

## 2. How is the "Down arrow" used in probability calculations?

The "Down arrow" is used in probability calculations to indicate the relationship between two events, where the probability of one event is dependent on the occurrence of another event.

## 3. Can the "Down arrow" be used in other areas of science besides probability?

Yes, the "Down arrow" symbol has various uses in different fields of science. It can represent the direction of a vector in physics or indicate a decrease in temperature in chemistry, among other uses.

## 4. What is the difference between the "Down arrow" and the "Up arrow" in probability?

The "Down arrow" represents conditional probability, while the "Up arrow" represents the inverse of conditional probability. In other words, the "Down arrow" is used when the probability of one event depends on another event, while the "Up arrow" is used when the probability of one event affects the probability of another event.

## 5. How can I remember the meaning of the "Down arrow" in probability?

A helpful way to remember the meaning of the "Down arrow" is to think of it as a downward flow of information. The probability of the second event is affected by the first event, which is represented by the downward direction of the arrow.

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