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I am preparing GRE Test which has Math Part.

How to solve probability questions in a real quick ?

One marble is randomly selected from a bag that contains only 4 black marbles, 3 red marbles, 5 yellow marbles, and 4 green marbles.

Quantity a) The probability of selecting either a black marble or a red marble Quantity b) The probability of selecting either a yellow marble or a green marble

Whether Quantity a will be greater ? Whether Quantity b will be greater ? Whether two Quantities are equal ? Relationship cannot be determined?

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closed as off-topic by 1999, Micah, Claude Leibovici, Hippalectryon, drhab Jul 2 '15 at 14:47

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Are you sure you describe the question correctly? Do you mean "4 black marbles"? – aelguindy Mar 1 '12 at 21:32
up vote 5 down vote accepted

I assume you mean the bag contains 4 black marbles.

There are 16 marbles total and we assume that outcomes are equally likely. That is, we assume that any particular marble is just as likely to be chosen as any other. Then, since there are 16 marbles total, the probability of selecting any particular marble is $1/16$.

In general, if outcomes are equally likely, then to find the probability of an event $A$, compute $$\text { size of }A\over\text{total number of outcomes}.$$ In the above "size of $A$" is the number of outcomes that make up $A$.

For $A$ being the event "a black or red marble was chosen", the size is $7$, (one of the 4 black or one of the 3 red were chosen). So, the probability that a black or red marble was chosen is $ 7/16$.

If $A$ is the event the event "a yellow or green marble is chosen", the size of $A$ is 9, and the corresponding probability is $9/16$.

Obviously, the second quantity is the greater one (which could have been seen without doing any arithmetic, since the size of "yellow or green" is larger than the size of "black or red").

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Thank you !! Yes it is 4 Black marbles and answer is correct, quantity b is greater !! And thank you for solving the question. This helps me to solve similar problems – Medex Mar 3 '12 at 23:53

I am assuming you meant the bag "contains 4 black marbles, ..."

You select one marble out of 16 marbles. 7 marbles are red or black, therefore the probability that your pick is red or black is $7/16$.

The probability that it is yellow or green can be calculated either by counting the number of yellow and green marbles, in this case 9 and dividing by 16.

Or you can notice that the probability of being red or black and that of being yellow and green sum to one. Therefore, the probabolity you get yellow or green is $1 - 7/16 = 9/16$.

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yes i missed to mention 4 black marbles. But your definition doesnt say, whether Quantity A is greater or B is Greater or two quantities are equal or Relationship Undetermined !!! – Medex Mar 4 '12 at 0:00

There's no algorithm (ie solution machine) that you can use to solve probability questions. You have to think about each question.

Most GRE questions are about equally likely outcomes.
The probability is the number of outcomes favourable to the question, divided by the total number of possible outcomes.

In your question: there are 18 marbles, so there are 18 possible outcomes. For (a) Favourable outcomes are black or red. There are 7 such outcomes, so probability is 7/18 For (b) Favourable outcomes are yellow or green. There are 9 such outcomes, so probability is 9/18


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