A bag contains 6 red marbles, 9 blue marbles, and 5 green marbles. You withdraw
one marble, replace it, and then withdraw another marble. What is the
probability that you do NOT pick two green marbles?

We calculate this by first calculating the probability of FAILURE.  Then we
used Probability of SUCCESS = 1 - Probability of FAILURE.

In order to FAIL, we must pick both marbles green.

The probability of picking the first marble green = 

5 green marbles/(20 marbles) = 1/4

So 1/4 of the times we perform the experiment we will get a green marble first.

Now of those 1/4 of the times we do the experiment and get a green marble the
first time, 1/4 of those times we will also get a green marble the second time.

So that's 1/4 of 1/4 or 1/16 

So the probability of FAILING (getting a green marbles both times) is 1/16

Therefore the probability of SUCCEEDING (not getting a green marble both
times) = 1 - 1/16 or 15/16

Edwin
AnlytcPhil@aol.com