Final Answer:
The statements equivalent to the assertion "A and B are independent" are: P(A)P(B)=P(A and B), P(B|A)=P(B), and P(A|B)=P(A). So, the correct options are A.P(A)P(B)=P(A and B), D.P(B|A)=P(B), and H. P(A|B)=P(A).
Step-by-step explanation:
The assertion of independence between events A and B refers to scenarios where the occurrence of one event does not influence the probability of the other. Statement A (P(A)P(B)=P(A and B)) represents the multiplication rule for independent events in probability theory, indicating that the probability of both A and B happening equals the product of their individual probabilities.
Statement D (P(B|A)=P(B)) signifies that the probability of event B occurring given event A has already happened is equal to the probability of B occurring independently of A. Statement H (P(A|B)=P(A)) suggests that the occurrence of event B does not affect the probability of event A happening.
These statements encapsulate different facets of the definition of independence between events. They indicate that the likelihood of A and B occurring together is not influenced by the occurrence of either event individually or when one event is known to have occurred. Each statement essentially articulates the idea that the occurrence of one event does not affect the likelihood of the other event happening, thus establishing the equivalence to the assertion of independence between events A and B.
So, the correct options are A.P(A)P(B)=P(A and B), D.P(B|A)=P(B), and H. P(A|B)=P(A).