vaibhav101 wrote:there were initially no black marbles in a jar. Subsequently, new marbles were added to the jar. If marbles are drawn at random and selected marbles are not returned to the jar, what is the probability of selecting 2 black marbles in a row?

1) after the new marbles are added, 50 % of all marbles are black.
2) among the 10 added marbles 8 are black.

We are given that "there were initially no black marbles in a jar." You need not assume that there were no marbles; there may or may not be few non-black marbles already in the jar.

Do not misread the information, "Subsequently, new marbles were added to the jar," as "Subsequently, new black marbles were added to the jar.

We have to find out the probability of selecting 2 black marbles in a row.

Let's take each statement one by one.

1) after the new marbles are added, 50 % of all marbles are black.

Say, now, there are 2x marbles in the jar; thus, there are x black and x non-black marbles in the jar.

Probability of selecting 2 black marbles in a row = [x/2x]*[(x - 1)/(2x - 1)] = (x - 1)/2(2x - 1)

We do not have the value of x. Insufficient.

2) among the 10 added marbles 8 are black.

We do not know how many marbles were already there in the jar. Insufficient.

(1) and (2) together

Since the after the new marbles are added, 50% of all marbles are black and among the 10 added marbles 8 are black, the number of non-black marbles and that of black marbles is 8 each.

=> x = 8

Probability of selecting 2 black marbles in a row = (x - 1)/2(2x - 1) = (8 - 1)/2(2*8 - 1) = 7/(2*15) = 7/30. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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