A urn has 3 red marbles, 2 blue marbles, 1white, 1 black 1 brown. What is the probability of getting exactly 1 red marble than not 1 red marble? What is the probability of getting at least 1 red marble?
I could not find a way to solve this question without listing the sample spaces. It's $2\bigg(\dfrac{3}{8} \cdot \dfrac{2}{7}\bigg)$ for the 1st one and for the 2nd one I asked what is the probability of not getting a red marble and took the compliment and get, $1-\dfrac{5}{8} \cdot \dfrac{4}{7}$ my question is why do I mulitply by 2 on the 1st question? I know there are 2 ways to get exactly 1 red marble but there are also 2 ways to not get a red marble right? How can I do this problem using combinations because this is a little shady to me.
You need to clearly specify how you draw. Without this, there is no answer. If you draw two marbles without replacement and are asking the chance that the first is red and the second is not, you just have the multiplication law: $\frac 38$ for the first red, then $\frac 57$ that the second is not (given that the first was red).