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Conditional probability focuses on the likelihood of an event occurring given that another, related event has already happened. The notation for this is P(A|B), read as "the probability of A given B," which is calculated as the probability of both A and B occurring (P(A and B)) divided by the probability of B occurring (P(B)) [-]. This formula effectively narrows the focus from the entire sample space to only those outcomes where event B is known to have happened [-]. Unlike standard probability where we implicitly divide by 1 (the probability of the entire sample space), conditional probability demands we account for the reduced certainty introduced by knowing B has occurred [-].
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Conditional probability focuses on the likelihood of an event occurring given that another, related event has already happened. The notation for this is P(A|B), read as "the probability of A given B," which is calculated as the probability of both A and B occurring (P(A and B)) divided by the probability of B occurring (P(B)) [-]. This formula effectively narrows the focus from the entire sample space to only those outcomes where event B is known to have happened [-]. Unlike standard probability where we implicitly divide by 1 (the probability of the entire sample space), conditional probability demands we account for the reduced certainty introduced by knowing B has occurred [-].