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## GMAT - Data Sufficiency - Probability

### Each of the marbles in a jar is either red or white or blue (more)

Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue?

(1) There are a total of 24 marbles in the jar, 8 of which are red.
(2) The probability that the marble selected will be white is 1/2.

Assume number of red balls is R, blue balls B and white balls W

1.

There are a total of 24 marbles in the jar, 8 of which are red.

24 = R + B + W

R = 8

B + W = 16 ... Eq. 1

Probability that one marble drawn is blue = B/24 = (16 - W)/24

we don't know the values of either B or W hence the statement is insufficient

2.

The probability that the marble selected will be white is 1/2.

Total Number of balls = R + B + W

Probability of drawing a white ball = W/(R + B + W)

1/2 = W/(R + B + W)

W = (R + B + W)/2

W = R + B ... eq 2

we do not know anything about B or R

hence the statement is insufficient. to calculate B

Combining both

R = 8

B + W = 16 ... 3

and R + B = W

8 + B = W

W - B = 8 ...4

from equations 3 and 4

2B = 8

B = 4

Probability of drawing a blue ball = 4/24 = 1/6