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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Wed Aug 06, 2014 7:42 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

Alternatively, we can use the COMPLEMENT.
That is, P(Event A happening) = 1 - P(Event A not happening)

So, P(selected marble is EITHER red or blue) = 1 - P(selected marble is NEITHER red nor blue)
= 1 - P(selected marble is either white or green)
= 1 - [P(marble is white) + P(marble is green)]
= 1 - [1/4 + 1/3]
= 1 - [3/12 + 4/12]
= 1 - 7/12
= 5/12

Cheers,
Brent

_________________
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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11187 messages
Followed by:
1221 members
5254
GMAT Score:
770
Wed Aug 06, 2014 7:37 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
...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

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

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