Question 171130
The probability of anything is the number of ways that you can be successful divided by the total number of ways something can happen.  In your case you have 64 total marbles, so if you draw one marble, there are 64 equally likely possibilities.  Since there are only 16 red marbles, only 16 of those 64 ways represent successfully drawing a red marble.  Your probability is therefore {{{16/64}}} which reduces to {{{1/4}}}.  The odds are calculated a little differently.  For your situation, you have 16 ways out of 64 that you can be successful and 48 ways that you can be unsuccessful, therefore the odds are 16:48 or 1:3.  That means that if you repeatedly pull out one marble and replace it, over the long term you will pull a red marble one time and a white marble three times out of every four pulls, on the average.  That is not to say that it couldn't happen that you pulled, say, 10 red marbles in a row -- it just wouldn't be very likely to happen.


Hope that helps.