Probability: drawing colored marbles from bag w/ replacement

[jdom543]

So I'm a bit confused with this question. I think I have it right I just would like someone to verify that it's correct.

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

So I think the answer is .657 or 65.7% Can anyone check this to see if it's correct.

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.

[maggiemagnet]

...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?

[jdom543]

I was referring to another problem entirely. The numbers that for the probabilities I got from a chart and rather then typing the chart I'll just give you the part I'm having trouble with.

If two events are independent then P(A) x P(B) = P(A and B).

So I came across a problem where I was supposed to prove whether or not something was independent or not. I got P(A) x P(B) is approximately .4565 and P(A and B) is approximately .4560. P(A and B) was given in the chart, as were P(A) and P(B) If the two events were independent then .4565 should equal .4560. But is the difference within reason to say that it's equal and the events are independent or to be independent, do they have to be EXACTLY equal to one another?

[maggiemagnet]

Technically, yes, they values should be exact. But if you have only approximate values, or if you rounded, then it might not work out exactly. You should probably ask your teacher for the rule for your class.