We can use inclusion-exclusion with conditional probabilities of the form P(A∪B∣C). Can we also do this when the union is on the "right-hand side" of the condition (giving the following formula)? Why or why not? P(A∣B∪C)=P(A∣B)+P(A∣C)−P(A∣B∩C)
We can use inclusion-exclusion with conditional
Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to which a probability is assigned. A single outcome is an element of a sample space and different events in a random experiment are generally not equally likely, since they may include very different groups of outcomes.
Union of Two Events: For any two events A and B, union of A and B, written as , is defined as the occurrent of either A or B or both. In other words, it is the occurrent of at least one of A and B.
Intersection of Two Events: For any two events A and B, intersection of A and B, written as , is defined as the occurrent of A and B both.
Conditional Probability: Let A and B be two events with P(A) > 0. Then the conditional probability of B given A, denoted by P(B | A), is defined as the probability of occurrent of the event B when it is assumed that the event A has already been occurred. It is given by the formula,
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