A bag contains five blue marbles, five red marbles, five white marbles, and five black marbles. You draw a marble from the bag, and then draw another marble from the bag.

Do you have a greater probability of drawing two blue marbles if you replace the first marble after you draw it or if you don't replace the marble?

Your answer should include both the mathematical proof and a written statement.

The probability of drawing a blue marble at first is 5/20. If you then replace this marble, the probability doesn't change, it's still 5/20. To get the probability of getting two blue marbles and not replacing we multiply :

5/20 * 5/20 = 25/400 = 1/16

Drawing 2 blue marbles while NOT replacing the first probability :

The probability of first choosing a blue marble is 5/20, but you don't replace it, so now the probability of choosing a blue marble is 4/19, since one blue marble was taken. To find the probability of drawing two blue marbles but not replacing the first one we are going to have to multiply 5/20 * 4/19. That's 1/19.

So the probability of getting two blue marbles and replacing the first is 1/16, and the probability of getting two blue marbles and not replacing the first is 1/19. Well, which is greater? 1/16 is greater. If you replace the first marble, you have a higher chance of picking two blue marbles.

Written Statement :

If you replace the first marble you have a higher chance of getting two blue because you are increasing the number of blue marbles in the 20 total marbles. Now there is a greater number of blue marbles there is a greater chance you will pick blue.