Mustcrackgmat wrote:A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?
(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125.
(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.
Statement 2 gives me the prob of one single marble NOT being blue. How can statement 2 help me calculating the prob of marble BEING blue? There are seven colors, so am not sure if I can apply 1-2/5 logic here.
P(blue) + P(not blue) = 1.
Let P(blue) = x/y and P(not blue) = a/b.
Thus:
x/y + a/b = 1.
Statement 1: The probability that all of the next five marbles taken from the jar are blue is 243/3125.
Since P(blue) = x/y, we get:
(x/y) * (x/y) * (x/y) * (x/y) * (x/y) = 243/3125
(x/y)� = 243/3125
x/y = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.
Statement 2: The probability that none of the next five marbles taken from the jar are blue is 32/3125.
Since P(not blue) = a/b, we get:
(a/b) * (a/b) * (a/b) * (a/b) * (a/b) = 32/3125
(a/b)� = 32/3125
a/b = 2/5.
Since x/y + a/b = 1, we get:
x/y = 1 - a/b = 1 - 2/5 = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.
The correct answer is
D.
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