These are independent if the probability of A given B is equal to the probability of A. Then we could say A and B are independent because the probability of A, if this is true, then this means the probability of A given B actually isn't dependent on whether B happened or not. It's the same thing as the probability of A. This would lead to these events being independent. Also, if you had probability of B given A is equal to the probability of B, same argument. That would mean they're independent. Or if we said that the probability of A and B is equal to the probability of A times the probability of B, then these would also mean they're independent.