GRE Quantitative Data Analysis – Probability

[Author: Lakshmi Harikumar]
GRE quantitative section primarily checks your basic mathematics skills and your capability to solve problems using quantitative methods. When it comes to data analysis, it’s all well and good because high school mathematics knowledge helps you to crack most of the questions. If you are polishing your grip on quantitative questions, place emphasis on arithmetic algebra and geometry. Generally, very few questions come from Probability section. Once you become proficient in other sections, step into probability to give your confidence a great boost. The questions coming from probability mainly cover compound events, independent events, conditional probability, random variables and probability distribution.
To tackle most of the probability questions, use the basic probability equation,
Probability of an event P(E) = number of favorable outcomes/total number of outcomes
Single Trial Questions
This is a very basic kind of question which involves single selection from a group of objects. The below given is an example of the same.
Question: In a bag containing 19 red, 10 white, and 9 black pebbles, what is the probability of getting a red pebble on a single draw?
Solution: We can define the sample space for the event as, S= {R, W, B}, where R, W, B represents red, white and black pebbles respectively.
Here, the red pebble is the favorable outcome, so the numerator, that’s the number of favorable outcomes become 19. The total number of possibilities or the total number of outcomes in our question is the total number of pebbles. The total number of pebbles is 19+10+9=38.
Substituting values in the formula, we get, P(E) = 2
Independent events
Two events are called independent if the occurrence of one event does not affect the probability of other. Whereas if the incidence of an event affects the probability of another event, then the events are dependent.
Question: There is a red colored unbiased six-sided die and a blue colored unbiased six-sided die. At the same instant, both of the dice are rolled. Let A be the event that the number on the red die is even. Let B be the event that the number on the blue die is odd. Are the events independent?
Solution: We have to consider that, the outcome of the red die does not affect the outcome of a blue die and vice versa.
P(A) =1/2
P(B) =1/2
Hence, both the events are independent.
Multiple Trial Questions
Often, probability questions asked in the GRE won’t be confined to a single draw or trial, but involve multiple trial questions too. For an example, a question which involves drawing an element multiple times from the same group of elements, you have to distinguish between draws with replacement and draws without replacement. Let’s see the difference using a marble example:
Example: From a group of marbles, you have to select a marble, after noting its color, put back the marble into the group. Again, you select a marble, this is simply called drawing with replacement. Consider another case where you select a marble and put it aside. Then you draw another marble from the remaining group of marbles. This is called drawing without replacement.

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