Three marbles are drawn randomly WITH REPLACEMENT

Question

Three marbles are drawn randomly WITH REPLACEMENT from a box with 5 blue and 7
green marbles.
(a) What is the probability that all the marbles drawn are green?
(b) What is the probability that 2 of the marbles drawn are green?
(c) what is the probability that at least one marble is green ?

Answer 1

If you have 12 marbles total, and 7 of them are green, you have a 7/12 chance of drawing a green marble.

 

Because you are replacing the marble each time, the probability remains 7/12 each time.

 

To solve the problem, you multiple the probabilities.

 

a) (7/12) * (7/12) * (7/12)  = (343/1,728) = 0.198

 

b) (7/12) * (7/12)  =  (49/144) = 0.34

 

c) (7/12) = 0.583