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.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?