6.probability of one event given that another has occurred
The probability of one event occurring given that another has already occurred is known as the conditional probability
The probability of one event occurring given that another has already occurred is known as the conditional probability. It represents the likelihood of an event happening under specific conditions, typically denoted as P(A|B), where A and B are two different events.
To calculate the conditional probability, you need to determine the probability of the intersection of the two events and divide it by the probability of the given condition. The formula for conditional probability is:
P(A|B) = P(A ∩ B) / P(B)
Let’s break down the formula:
– P(A|B): This represents the conditional probability of event A occurring given that event B has occurred.
– P(A ∩ B): This is the probability of the intersection of events A and B. It shows the likelihood of both events A and B happening together.
– P(B): This is the probability of event B occurring, which serves as the given condition.
By dividing the probability of the intersection by the probability of the given condition, we obtain the conditional probability.
It’s important to note that the conditional probability is only applicable when the probability of event B is greater than zero (P(B) > 0). If P(B) is equal to zero, then the conditional probability is undefined.
Conditional probability is a fundamental concept in probability theory and is widely used in various fields, including statistics, economics, and decision analysis. It helps us make more accurate predictions and understand how events are influenced by prior knowledge or observations.
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