Final answer:
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. The probability of both events being less than one depends on whether the individual probabilities are less than one or equal to one. If both probabilities are less than one, then the statement is true, otherwise it is false.
Step-by-step explanation:
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. To determine if the statement is true or false, we need to consider the probability of both events being less than one. If events A and B are independent, then the probability of both events is the product of their individual probabilities: P(A and B) = P(A) * P(B). If both probabilities are less than one, then the statement is true. However, if either P(A) or P(B) (or both) is equal to one, then the statement is false. This is because if the probability of either event is equal to one, it means that event is certain to occur, and therefore the probability of both events occurring is one as well.