...So there's 3 red, 5 blue and 2 white marbles in a bag. You select 3 marbles with replacement. What is the Probability that you select at least 1 red marble?
So I think it should be set up like this:
P(At least 1 red marble)=1-P(No red marbles)=1-.7³ =.657
I agree with your set-up, with the probability of "at least one" being "100%, less the probability of none". Since there are 10 marbles, with three being red, then there is a 70% probability of drawing something else on each draw. Since this is "with replacement", each draw has the same probability. I get the same answer you do.
Also when you try to determine whether 2 things are independent of each or not. You can use P(A) x P(B) = P(AnB)
Then you solve it down to P(A) x P(B) = .4565 and P(AnB) = .4560 (given). Since there so close can you say they're independent or do they have to be exactly equal to one another.
I'm sorry, but I don't understand what you're doing here. Is this a second exercise? Where did the probabilities come from?