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Post subject: GMAT Probability Posted: Wed Sep 08, 2010 4:57 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

In a bag, there are N blue marbles, (4N + 12) red marbles, and 3 yellow marbles. If a single marble is removed from the bag, what is the probability that the marble will be blue or yellow?
A. 1/5 B. 1/4 C. 1/3 D. 1/2 E. 2/3
(A) To solve this problem, first calculate the total number of marbles in the bag: Blue marbles = N Red marbles = 4N + 12 Yellow marbles = 3 Total marbles (sum of blue, red and yellow) = 5N + 15.
Then determine the number of marbles that are either blue or yellow: Total of blue and yellow = N + 3.
Then the probability of removing a blue or yellow marble is: = (N + 3) / (5N + 15) = = (N + 3) / (5(N + 3)) = 1/5.
The correct answer is choice (A). 
Another option: Calculate probability of red and then minus this from 1.
Red = 4N+12 Total = 4N +12 + N + 3 = 5N + 15
Red/Total = 4/5
Complementary event = 1 – 4/5 = 1/5


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Gennadiy

Post subject: Re: math (test 2, question 35): probability Posted: Wed Sep 08, 2010 5:10 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498

That is true. It is a possible way though it doesn't give us any advantage in this case.
The events "1 removed marble is red" and "1 removed marble is blue or yellow" are mutually exclusive and exhaustive. (If we remove a marble it can be either red, blue or yellow. No other options are possible. Therefore one and only one event out of two will occur). Events that are mutually exclusive and exhaustive are called complementary events.
For complementary events it is always true that: [Probability of event 1] + [Probability of event 2] = 1
So [Probability we remove Red marble] + [Probability we remove blue or yellow marble] = 1.
It is a good method to use in many cases. However in this specific case it doesn't give us any advantage. The processes of finding probability of removing Red marble or finding probability of removing blue or yellow marble are equally easy.


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