You randomly select 2 marbles from a mug containing 7 blue marbles, 3 red marbles, and 2 white marbles. How many times greater is the probability of selecting 2 red marbles when you replace the first marble before selecting the second marble than when you do not replace the first marble before selecting the second marble?
Probability of drawing 2 red marbles if first marble is placed back in bag before second is drawn:
because (12 comes from total number of marbles)
Probability of drawing 2 red marbles without returning first back to bag:
Probability of drawing first (from above):
(New) Probability of drawing second:
(2 is new number of red marbles, 11 is new total number of marbles)
Multiply both probabilities (for total probability of drawing 2 red marbles without returning first to bag)