# Thread: Bag contains 3 red marbles and 2 black marbles

1. ## Bag contains 3 red marbles and 2 black marbles

Good afternoon, I'm having some issues with this problem. I would appreciate any help. Thank you!

1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?

2. ## Re: Bag contains 3 red marbles and 2 black marbles

Originally Posted by Schnoodle100
1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?
This is a good thought problem.

In order for $B$ to win it must occur on the first or third drawing. You need to really understand that logic.

What is the probability that $B$ wins on the first draw?

What is the probability that $B$ wins on the third draw?

3. ## Re: Bag contains 3 red marbles and 2 black marbles

2/5 on the first draw
Then something out of 3 for the 3rd draw

4. ## Re: Bag contains 3 red marbles and 2 black marbles

Originally Posted by Schnoodle100
Good afternoon, I'm having some issues with this problem. I would appreciate any help. Thank you!

1 Bag contains 3 red marbles and 2 black marbles. Two people, B, and C, take turns drawing a marbles from the bag without replacing any of the marbles picked. The 1st person to draw a black marble wins. What is the probability that person B, who always draws first, wins?
I don't see any shortcuts to this problem. You're going to have to just develop the entire probability tree for the sequence of outcomes and sum of the probabilities of person B winning.

here, you can chase down the probability of B winning.

5. ## Re: Bag contains 3 red marbles and 2 black marbles

Originally Posted by Schnoodle100
2/5 on the first draw YES
Then something out of 3 for the 3rd draw Maybe
On the third draw there are two conditions to consider:
did $C$ not win on the second draw and $B$ wins on the third.

6. ## Re: Bag contains 3 red marbles and 2 black marbles

So...I'm a little confused as to go about doing this problem

7. ## Re: Bag contains 3 red marbles and 2 black marbles

Originally Posted by Schnoodle100
So...I'm a little confused as to go about doing this problem
$\dfrac{2}{5}+\dfrac{3}{5}\dfrac{2}{4}\dfrac{2}{3}$

8. ## Re: Bag contains 3 red marbles and 2 black marbles

Alright thank you for all the help!