Math Problem: Probability

[bponfgtr]

I need help understanding how this problem is done... 

 

Suppose there are 9 blue marbles, 4 yellow marbles and 10 green marbles in a box. What is the probability of randomly selecting three green marbles with replacement? Show fractions (don't have to simplify final fraction) and then round to 4 decimal places. 

tampa bucs

I don't even know where to begin.

Edited January 1, 2017 by bponfgtr

[MarkT]

http://homepages.math.uic.edu/~bpower6/stat101/probability%20examples.pdf

[Monica_in_Switzerland]

With replacement are the simplest types of problems because the events are independent.  

 

So:  On your first draw, there is a 10/23.  That probability remains the same for each draw because you are always replacing the marble.  Next, you can imagine this as a chain of events.  

 

Chances on the first draw are 10/23.  On the second draw, it will be 10/23 x 10/23, and for the third draw, 10/23 x 10/23 x 10/23.  Or (10/23)^3

 

 

[Monica_in_Switzerland]

Often times, you would daw a probability tree to get a better idea of what is happening.  

 

 

Here's how the tree would start, but I didn't type out all of the third column because the formatting would take forever.  :-)  In bold is the desired outcome.  You multiply the odds of each event occurring as you go across to get your final probability for the chain of three events.  

 

 

1st draw       2nd draw             3rd draw

 

 

                     yellow                      (etc)

yellow           green

                     blue

 

                     yellow

green           green                         green

                     blue

 

 

 

                      yellow

blue               green

                      blue