Are you one of the many students who feel a pang of anxiety when faced with probability and statistics questions on the GRE? By mastering these concepts and adopting effective problem-solving strategies, you can transform those feelings of uncertainty into a sense of confidence. In this blog post, we will discuss key strategies for tackling probability and statistics questions on the GRE, providing you with a solid foundation to excel in this area.
In this blog:
- Working GRE Probability and Statistics Basics
- Knowing GRE Probability and Statistics Questions
- Visualising GRE Probability and Statistics Questions
- Solving GRE Probability and Statistics with Rules
- Learning GRE Probability and Statistics Tips
- Understanding GRE Probability and Statistics Types
Working GRE Probability and Statistics Basics
Build a Strong Foundation
Before diving into problem-solving techniques, it is crucial to have a firm grasp of the underlying probability and statistics concepts. Let’s say you encounter a probability question that involves rolling two dice. To understand the concept of probability, you need to know that each die has six sides numbered from 1 to 6. By understanding the concept, you can determine that the total number of possible outcomes is 6 x 6 = 36.
Familiarise yourself with terminology, probability rules, statistical measures, and key formulas. This includes topics such as:
- Probability: The likelihood that an event will occur.
- Statistics: The collection, analysis, and interpretation of data.
- Sets: A collection of objects.
- Probability distributions: A list of all the possible outcomes of an event and their associated probabilities.
- Random variables: A variable that can take on different values depending on the outcome of an event.
Also read: Mastering GRE Quantitative Comparison
Above it all, you need to develop an understanding of fundamental concepts like permutations, combinations, probability distributions, mean, median, and standard deviation.
Knowing GRE Probability and Statistics Questions
Analyse & Practise Different Question Types
Don’t skip this step! We need you to carefully read each question, paying attention to the details and requirements. Then identify the GRE Probability question format/ topic being tested, whether it’s probability, distributions, or statistical inference. Determine what the question is asking for and the given information. Underline the key data and variables to help you stay focused on the relevant information while solving the problem.
Consider a GRE statistics question that presents a dataset of test scores for two different groups of students. By analysing the question, you can identify whether it requires comparing the means of the two groups or determining the standard deviation.
Usually these are the types of GRE Probability questions you might encounter:
- Multiple choice: You’re given a question and a set of answer choices. You have to select the answer choice that best answers the question.
- Quantitative Comparison: You’re given two quantities and asked to compare them. You have to determine whether Quantity A is greater than Quantity B, Quantity B is greater than Quantity A, or the two quantities are equal.
- Numeric Entry: You’re given a question and a blank. You have to fill in the blank with the correct numerical answer.
Visualising GRE Probability and Statistics Questions
Put Some Daydreaming Skills Into Action
Probability and statistics problems often involve complex scenarios and multiple variables. To simplify the problem, try visualising the situation or representing it with a diagram or chart. This visual representation can help you organise the information and make it easier to identify the relationships between variables. Visual aids, such as tables, charts, or Venn diagrams, can be valuable tools for clarifying the problem and finding the most efficient solution.
Drawing diagrams can also be helpful for visualising statistics and GRE probability questions. This can make it easier to understand the problem.
Score GRE 325+ with this GRE Study Plan
Solving GRE Probability and Statistics with Rules
Use Some Handy Rules to Solve Faster
Probability questions on the GRE frequently involve applying fundamental rules like the multiplication rule, addition rule, conditional probability, and Bayes’ theorem. Familiarise yourself with these rules and understand when to apply each one. Take note of any given conditions or constraints and use them to modify the probability calculation accordingly. Practice applying these rules to a variety of problem types to develop a strong intuition for probability.
Here are five important probability rules that are commonly used in solving probability problems:
- Conditional Probability: Conditional probability measures the probability of an event A occurring given that another event B has already occurred. It is denoted as P(A|B) and can be calculated using the following formula:
P(A|B) = P(A and B) / P(B)
- Law of Total Probability: The law of total probability is used to calculate the probability of an event A by considering all possible ways that event A can occur. It states that if we have a set of mutually exclusive events B1, B2, …, Bn (i.e., the events cannot occur simultaneously), then the probability of event A can be calculated as the sum of the probabilities of A given each of the mutually exclusive events, multiplied by their respective probabilities. Mathematically, it can be expressed as:
P(A) = P(A|B1) x P(B1) + P(A|B2) x P(B2) + … + P(A|Bn) x P(Bn)
- Bayes’ Theorem: Bayes’ theorem allows us to update the probability of an event A given new evidence B. It states that the probability of event A given evidence B can be calculated using the conditional probability of B given A, multiplied by the prior probability of A, divided by the probability of evidence B. Mathematically, it can be expressed as:
P(A|B) = (P(B|A) * P(A)) / P(B)
Suggested Read: GRE Score Percentiles: know everything
Learning GRE Probability and Statistics Tips
Utilise Combinatorics Techniques
Imagine you need to solve a probability question that involves arranging a group of people in a row. By understanding permutations, you can calculate the number of possible arrangements based on the given conditions, such as considering or ignoring the order of certain individuals.
Combinatorics, the branch of mathematics that deals with counting and arranging objects, is often relevant to probability questions on the GRE. Understand the concepts of permutations and combinations and learn how to identify when these techniques should be employed. Practice problems that involve arranging items in a specific order or selecting items from a group to strengthen your combinatorics skills.
Understanding GRE Probability and Statistics Types
Study Probability Distributions
Familiarise yourself with common probability distributions such as the binomial, normal, and Poisson distributions. Understand their properties, formulas, and appropriate applications. Work on problems that involve finding probabilities based on these distributions, as well as problems that require you to interpret and analyse data using statistical measures derived from these distributions.
Consider a statistics question that involves the distribution of heights among a group of people. By understanding the properties of the normal distribution, you can determine the probability of finding an individual within a specific height range based on the mean and standard deviation.
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