What does the equation p(A∪B) = p(A) + p(B) - p(A∩B) represent?

What does the equation p(A∪B) = p(A) + p(B) - p(A∩B) represent?

• A. Joint probability that events A and B will occur
• B. Addition rule
• C. Conditional probability that event B will occur
• D. Multiplication rule

Answer: (B)

The equation \( p(A∪B) = p(A) + p(B) - p(A∩B) \) represents the addition rule in probability, which is crucial for understanding how to calculate the probability of the occurrence of at least one of two events, A or B. This equation accounts for the potential overlap between the two events by subtracting the probability of both events occurring simultaneously, which is represented by \( p(A∩B) \). When calculating probabilities for two events, it's important to recognize that simply adding \( p(A) \) and \( p(B) \) could lead to double-counting the scenarios where both A and B occur. Therefore, this rule ensures that we accurately reflect the total probability of either event happening without redundancy. The addition rule helps in various applications in healthcare statistics, where the probability of multiple events is often evaluated. Thus, the selection of the addition rule as the correct answer appropriately identifies the purpose and function of the equation in question.

The equation ( p(A∪B) = p(A) + p(B) - p(A∩B) ) represents the addition rule in probability, which is crucial for understanding how to calculate the probability of the occurrence of at least one of two events, A or B. This equation accounts for the potential overlap between the two events by subtracting the probability of both events occurring simultaneously, which is represented by ( p(A∩B) ).

When calculating probabilities for two events, it's important to recognize that simply adding ( p(A) ) and ( p(B) ) could lead to double-counting the scenarios where both A and B occur. Therefore, this rule ensures that we accurately reflect the total probability of either event happening without redundancy. The addition rule helps in various applications in healthcare statistics, where the probability of multiple events is often evaluated.

Thus, the selection of the addition rule as the correct answer appropriately identifies the purpose and function of the equation in question.