## There is a total of 120 marbles in a box, each of which is red, green, blue, or white.

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### There is a total of 120 marbles in a box, each of which is red, green, blue, or white.

by BTGModeratorVI » Sat Jun 27, 2020 6:42 am

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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

Source: GMAT paper tests

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### Re: There is a total of 120 marbles in a box, each of which is red, green, blue, or white.

by [email protected] » Tue Jun 30, 2020 5:58 am
BTGModeratorVI wrote:
Sat Jun 27, 2020 6:42 am
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

Source: GMAT paper tests
...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

Cheers,
Brent

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### Re: There is a total of 120 marbles in a box, each of which is red, green, blue, or white.

by [email protected] » Mon Apr 19, 2021 6:12 am
BTGModeratorVI wrote:
Sat Jun 27, 2020 6:42 am
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

Source: GMAT paper tests
Solution:

We need to determine P(red or blue). Since the each marble white, green, red or blue (and no marbles have more than one color), we can create the equation:

P(white) + P(green) + P(red) + P(blue) = 1

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

P(red) + P(blue) = 1 - 1/3 - 1/4 = 5/12

Since each marble has only one color, P(red or blue) = P(red) + P(blue). Thus, P(red or blue) = 5/12.