Problem Solving

AAPL wrote:GMAT Paper Tests

There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue?

A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 5/12

OA E

...the probability that it [the marble] will be white is 1/4
So, 1/4 of the 120 marbles are white.
In other words, there are 30 white marbles.

...the probability that it [the marble] will be green is 1/3
So, 1/3 of the 120 marbles are green .
In other words, there are 40 green marbles.

Altogether, there are 70 marbles that are EITHER white or green.
This means that the remaining 50 marbles are EITHER red or blue.

So, P(selected marble is EITHER red or blue) = 50/120 = 5/12

Answer: E

Cheers,
Brent

AAPL wrote:GMAT Paper Tests

There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue?

A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 5/12

We see that there are 120 x 1/4 = 30 white marbles and 120 x 1/3 = 40 white marbles, so there must be 120 - 70 = 50 blue or red marbles.

So the probability of selecting either a red or blue marble is 50/120 = 5/12.

Alternate solution:

Since P(red) + P(green) + P(blue) + P(white) = 1 and P(green) = 1/3 and P(white) = 1/4, we have:

P(red) + 1/3 + P(blue) + 1/4 = 1

P(red) + P(blue) = 1 - 1/3 - 1/4

P(red or blue) = 5/12

Answer: E