Final answer:
The equation that justifies whether events A and B are independent is P(A AND B) = P(A)P(B). If this equation holds, then the events are independent; if not, they are dependent.
Step-by-step explanation:
To determine whether the events A and B are dependent or independent, we need to apply the correct probability rule. The multiplication rule for independent events tells us that if A and B are independent, then P(A AND B) = P(A)P(B). Therefore, the equation that justifies whether the events are independent is:
A. P(A∩B)=P(A)⋅P(B)
Furthermore, if the above equation holds true, then events A and B are independent. Otherwise, they are dependent. Let us also consider the other options provided in the question:
- B. P(A∩B)=P(A)+P(B) - This equation would be true if events A and B are mutually exclusive, not independent.
- C. P(A∧B)=P(A) - This expression is incorrect as it is written in a way that doesn't make sense in probability theory.
- D. P(A∧B)=P(A∩B) - This equation is true but it doesn't relate to independence; instead, it follows from the definition of conditional probability.