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1. A jar has 10 marbles, a combination of black and white. 2 marbles are randomly chosen
from the jar. If q is the probability that both will be black, is q > 1/3?
(1) Less than 1/2 of the marbles in the jar are white.
(2) The probability that 1 white marble and 1 black marble will be chosen together
is 7/15.
(A) Statement (1) BY ITSELF is sufficient to answer the question, but statement
(2) by itself is not.
(B) Statement (2) BY ITSELF is sufficient to answer the question, but statement
(1) by itself is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question,
even though NEITHER statement BY ITSELF is sufficient.
(D) Either statement BY ITSELF is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question,
meaning that further information would be needed to answer the question.
Solution
This is a dependent probability problem. If you want to find the probability
of choosing 2 black marbles, you will need to figure out the probability that
the first marble will be black and that the second marble will be black. In
this case, the question wants to know if that probability is larger than 1/3.
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