If you are randomly sampling one at a time with replacement from a bag of marbles that contains 8 blue marbles, 7 red marbles and 5 green marbles, what is the probability of obtaining at least 2 red marbles in 3 draws from the bag. I know if I needed the first 2 to be red (with replacement) I would use:

(7/20)(7/20)= 49/400 = .1225

I am confused with this 3 draws piece. Am I using p(a)p(b)p(c)?

Any help showing me the right direction would be appreciated.

Picking at least two red balls from the 3 first draws means that you have many different possibilities, namely,

RRR
RBR
RGR
GRR
BRR
RRG
RRB

as combinations. (R-red marble, B-blue marble, G-green marble)

Find each probability, and add them up, because it is then and 'either-or' case.

I hope this helped! :)

Answer question10-11 based on the following: A jar contains 15 lollipopd: 6 red, 2 green, 4 blue, and 3 yellow.

1. A blue followed by a red. (2 lollipops are chosen with replacement.)

11. At least one green. (three lollipops are chosen with replacement.)

1. Multiply the probability of having a blue lollipop by that of having a red lollipop.

11. Take the probability of having no green at all from the three you take. Then, subtract that from 1.

Quote:

---

Originally Posted by bart10127

If you are randomly sampling one at a time with replacement from a bag of marbles that contains 8 blue marbles, 7 red marbles and 5 green marbles, what is the probability of obtaining at least 2 red marbles in 3 draws from the bag. I know if I needed the first 2 to be red (with replacement) I would use:

(7/20)(7/20)= 49/400 = .1225

I am confused with this 3 draws piece. Am I using p(a)p(b)p(c)?

Any help showing me the right direction would be appreciated.

---

If you are sampling WITH replacement, then this means that the probability of drawing red in EACH draw is a constant (7/20) and of not drawing red is also a constant (13/20)

Then if X is defined as the number of red marbles in three draws,

X follows a binomial distribution with p = 7/20 and q = 13/20 and n = 3

The general formula is P(X=r) = nCr x q^(n-r) x p^r

For P(X is at least 2), you will need P(X=2) + P(X=3)