You select a marble without looking and then put it back. If you do this 20 times, what is the best prediction possible for the number of times you will pick a purple marble?

Since you are selecting the marble without looking, the best prediction possible for the number of times you will pick a purple marble is 20 times. This is because each time you select a marble, there is an equal chance of picking any color, so on average, you would expect to pick a purple marble 1 out of every 1 times.