micromass said:I interpet it as the first. And you're right, the second expression doesn't make much sense...
P(A and B|C) refers to the probability of both events A and B occurring, given that event C has already occurred. It is a conditional probability that takes into account the information provided by event C.
The formula for calculating P(A and B|C) is: P(A and B|C) = P(A|C) * P(B|C), where P(A|C) represents the probability of event A occurring given that event C has occurred, and P(B|C) represents the probability of event B occurring given that event C has occurred.
The relationship between P(A and B|C) and P(A|C) and P(B|C) can be understood as follows: P(A and B|C) is equal to the product of P(A|C) and P(B|C) when A and B are independent events. However, if A and B are dependent events, then P(A and B|C) may not be equal to the product of P(A|C) and P(B|C).
No, P(A and B|C) cannot be greater than 1. The probability of an event cannot exceed 1, as it represents the certainty of the event occurring. If P(A and B|C) is greater than 1, it would mean that the events A and B are always occurring together, which is not possible.
P(A and B|C) is commonly used in scientific research to analyze the relationships between different variables or events. It allows researchers to understand how the occurrence of one event may affect the probability of another event. By calculating and interpreting P(A and B|C), scientists can make informed decisions and draw conclusions based on the data they have collected.