Substitute the given numerical values into the rearranged formula P(B|A) = P(B)P(A|B)/P(A). For example, if P(B)=1/21, P(A|B) = 4/10, and P(A)=24/210, the calculation is (1/21∗4/10) / (24/210).
Conditions: The formula used is the rearranged Bayes identity for P(B|A).; The given probabilities must be consistent with the formula's assumptions (e.g., P(A)>0).
Substitute the given numerical values into the rearranged formula P(B|A) = P(B)P(A|B)/P(A). For example, if P(B)=1/21, P(A|B) = 4/10, and P(A)=24/210, the calculation is (1/21∗4/10) / (24/210).
Conditions: The formula used is the rearranged Bayes identity for P(B|A).; The given probabilities must be consistent with the formula's assumptions (e.g., P(A)>0).
Starting from the equality P(A)P(B|A) = P(B)P(A|B), you can solve for either conditional probability by dividing by the corresponding marginal probability. Dividing both sides by P(B) isolates P(A|B), giving P(A|B) = P(A)P(B|A)/P(B).
Conditions: Both A and B have positive probability for the ordinary conditionals used here.; The algebraic rearrangement requires the denominators P(B) and P(A) to be nonzero.
Starting from the equality P(A)P(B|A) = P(B)P(A|B), you can solve for either conditional probability by dividing by the corresponding marginal probability. Dividing both sides by P(B) isolates P(A|B), giving P(A|B) = P(A)P(B|A)/P(B).
Conditions: Both A and B have positive probability for the ordinary conditionals used here.; The algebraic rearrangement requires the denominators P(B) and P(A) to be nonzero.