A magical leather pouch contains 2 alabaster marbles, 3 cerulean marbles, and 5 magenta marbles. First, four marbles are

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Tue Feb 09, 2021 8:09 am

Magoosh

A magical leather pouch contains 3 alabaster marbles, 3 cerulean marbles, and 5 magenta marbles. First, four marbles are removed at random, without replacement. Next, three more marbles are removed at random, without replacement. What is the probability that the remaining marbles are the same color?

A. 1/7
B. 1/8
C. 1/120
D. 7/120
E. 11/120

OA E

Solution:

We see that after 7 of the 10 marbles are removed, if the remaining 3 marbles are the same color, then they must be either all cerulean or all magenta, as these are the only two colors that have at least 3 marbles.

Case 1: The last 3 marbles are cerulean

This means the first 7 marbles that are removed consist of 2 alabaster marbles and 5 magenta marbles. The probability that these marbles are removed is:

(2C2 x 5C5)/(10C7) = (1 x 1)/120 = 1/120

Case 2: The last 3 marbles are magenta

This means the first 7 marbles that are removed consist of 2 alabaster marbles, 3 cerulean marbles and 2 magenta marbles. The probability that these marbles are removed is:

(2C2 x 3C3 x 5C2)/(10C7) = (1 x 1 x 10)/120 = 10/120

Therefore, the total probability is 1/120 + 10/120 = 11/120.

Answer: E