Question

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 one blue marble and then one red marble when you do not replace the first marble before selecting the second marble than when you do replace the first marble before selecting the second marble? Express the answer as a fraction.

Answer 1

Scenario 1: w/o replacement: P(blue, then red) = (7/12)(3/11) = 7/44

Scenario 2: w/ replacement: P(blue, then red) = (7/12)(3/12) = 7/48

Ratio of Probability #1 to Probability # 2 = 48/44 = 12/11, i.e. Prob # 1 is 1.0909... times Prob # 2

Explanation: