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rabbed
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Is it possible to solve something like this generally or does it depend on the pdf's of the variables?
P(x < f(y) | x > -f(y))
P(x < f(y) | x > -f(y))
A conditional probability is the likelihood of an event occurring given that another event has already occurred. It is denoted by P(A|B), where A is the event of interest and B is the condition.
A conditional probability is calculated by dividing the probability of the joint occurrence of both events (P(A∩B)) by the probability of the condition (P(B)). In formula form, it is written as P(A|B) = P(A∩B) / P(B).
If two events A and B are independent, then the conditional probability of A given B is equal to the probability of A. In other words, the occurrence of event B does not affect the likelihood of event A. However, if two events are not independent, then the conditional probability of A given B may be different from the probability of A.
Conditional probability is used in a variety of fields, including medicine, finance, and weather forecasting. For example, in medicine, it can be used to determine the chance of a patient having a certain disease given their age and other risk factors. In finance, it can be used to calculate the probability of different investment outcomes based on market conditions. In weather forecasting, it can be used to predict the likelihood of a hurricane given certain meteorological conditions.
Conditional probability calculates the likelihood of an event given that another event has already occurred, while joint probability calculates the likelihood of two events occurring together. In other words, conditional probability is a subset of joint probability. Additionally, conditional probability uses the probability of the condition in its calculation, while joint probability uses the probability of both events occurring simultaneously.