Easy GRE Probability Word Problems Practice Questions

Probability measures the likelihood of a specific event occurring, expressed as a ratio between zero and one. In the context of the GRE General Test, Easy GRE Probability Word Problems typically focus on the fundamental definition of probability and simple independent events. Understanding how to translate a word problem into a fraction is the most critical skill for success in this area of the GRE Prep curriculum.

According to Khan Academy, the basic formula for probability is the number of successful outcomes divided by the total number of possible outcomes. While the math itself is often straightforward, the GRE uses word problems to test your ability to identify which numbers belong in the numerator and which belong in the denominator. Practicing with GRE practice questions with answers helps build the intuition needed to spot these relationships quickly during the timed exam.

Concept Explanation

Probability is defined as the numerical representation of the chance that a specific outcome will happen out of all possible outcomes. The core formula used for almost every easy-level problem is:

$$P(E) = \ \frac{\ \text{Number of favorable outcomes}}{\ \text{Total number of possible outcomes}}$$

When solving Easy GRE Probability Word Problems, you must follow these three steps:

1. Identify the Total: Determine the size of the entire set (the sample space). This is your denominator.
2. Identify the Target: Determine how many items in that set meet the specific criteria mentioned in the problem. This is your numerator.
3. Simplify: GRE answers are almost always in simplest fractional form, though they can occasionally appear as decimals or percentages.

It is also important to remember the "Complement Rule." The probability of an event happening plus the probability of it not happening always equals 1. If the probability of rain is $\ \frac{1}{4}$, the probability of no rain is $1 - \ \frac{1}{4} = \ \frac{3}{4}$. This trick is frequently useful when a problem asks for the probability of "at least one" or "not" a certain outcome. For more complex variations, you might explore unlimited GRE practice questions to see how these basics evolve into harder multi-step problems.

Solved Examples

Example 1: A jar contains 5 red marbles, 8 blue marbles, and 7 green marbles. If one marble is chosen at random, what is the probability that it is blue?

1. Find the total number of marbles: $5 + 8 + 7 = 20$.
2. Identify the favorable outcomes (blue marbles): 8.
3. Set up the fraction: $\ \frac{8}{20}$.
4. Simplify the fraction by dividing both numbers by 4: $\ \frac{2}{5}$.
5. Answer: $\ \frac{2}{5}$.

Example 2: A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

1. Identify the total possible outcomes on a six-sided die: {1, 2, 3, 4, 5, 6}, so the total is 6.
2. Identify the favorable outcomes (numbers > 4): {5, 6}, so there are 2 favorable outcomes.
3. Set up the fraction: $\ \frac{2}{6}$.
4. Simplify: $\ \frac{1}{3}$.
5. Answer: $\ \frac{1}{3}$.

Example 3: In a class of 30 students, 12 are wearing glasses. If a student is selected at random, what is the probability that the student is NOT wearing glasses?

1. Find the number of students not wearing glasses: $30 - 12 = 18$.
2. Identify the total number of students: 30.
3. Set up the fraction: $\ \frac{18}{30}$.
4. Simplify by dividing by 6: $\ \frac{3}{5}$.
5. Answer: $\ \frac{3}{5}$ or 0.6.

Practice Questions

1. A bag contains 4 red pens, 6 black pens, and 10 blue pens. What is the probability of picking a red pen at random?

2. A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability that the spinner lands on a prime number?

3. A box contains 50 light bulbs, of which 4 are defective. If one bulb is selected at random, what is the probability that it is NOT defective?

4. A card is drawn from a standard deck of 52 playing cards. What is the probability that the card is a Heart?

5. If a letter is chosen at random from the word "PROBABILITY", what is the probability that it is a vowel?

6. A committee consists of 4 men and 6 women. If one person is chosen to be the chairperson, what is the probability that a woman is chosen?

7. A pair of fair coins is tossed. What is the probability that both coins land on heads?

8. A drawer contains 10 white socks and 10 black socks. If one sock is pulled out, what is the probability it is white?

9. A set of integers contains {2, 4, 6, 8, 10, 12, 14, 16}. If one number is picked, what is the probability it is a multiple of 4?

10. A restaurant offers 3 types of appetizers and 5 types of main courses. If a customer picks one of each at random, how many total combinations are possible, and what is the probability of picking one specific combination?

Answers & Explanations

1. Answer: 1/5. Total pens = 4 + 6 + 10 = 20. Favorable outcomes (red) = 4. Probability = $\ \frac{4}{20} = \ \frac{1}{5}$.

2. Answer: 1/2. Total sections = 8. Prime numbers between 1 and 8 are {2, 3, 5, 7}, which are 4 numbers. Probability = $\ \frac{4}{8} = \ \frac{1}{2}$.

3. Answer: 23/25. Total bulbs = 50. Non-defective bulbs = $50 - 4 = 46$. Probability = $\ \frac{46}{50} = \ \frac{23}{25}$. You can also use the AI Question Generator to practice similar complement-rule problems.

4. Answer: 1/4. Total cards = 52. Total Hearts = 13. Probability = $\ \frac{13}{52} = \ \frac{1}{4}$.

5. Answer: 4/11. The word "PROBABILITY" has 11 letters. The vowels are O, A, I, I (4 vowels). Probability = $\ \frac{4}{11}$.

6. Answer: 3/5. Total people = 4 + 6 = 10. Total women = 6. Probability = $\ \frac{6}{10} = \ \frac{3}{5}$.

7. Answer: 1/4. The possible outcomes for two coins are {HH, HT, TH, TT}. There are 4 total outcomes. Only 1 is "HH". Probability = $\ \frac{1}{4}$.

8. Answer: 1/2. Total socks = 20. White socks = 10. Probability = $\ \frac{10}{20} = \ \frac{1}{2}$.

9. Answer: 1/2. Total numbers = 8. Multiples of 4 in the set are {4, 8, 12, 16}, which is 4 numbers. Probability = $\ \frac{4}{8} = \ \frac{1}{2}$.

10. Answer: 1/15. Total combinations = $3 \ \times 5 = 15$. Any one specific combination has a probability of $\ \frac{1}{15}$.

1. A bag contains 3 red, 4 blue, and 5 yellow marbles. What is the probability of selecting a marble that is NOT red?

• A1/4
• B3/4
• C1/3
• D2/3

Frequently Asked Questions

What is the difference between probability and odds?

Probability is the ratio of favorable outcomes to the total outcomes, whereas odds are the ratio of favorable outcomes to unfavorable outcomes. For example, if the probability of winning is 1/5, the odds of winning are 1 to 4.

Can a probability value be greater than 1?

No, a probability value must always be between 0 and 1, inclusive. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain to occur.

How do you calculate the probability of two independent events both happening?

To find the probability of two independent events occurring together, you multiply their individual probabilities. For instance, the probability of flipping two heads in a row is 1/2 times 1/2, which equals 1/4.

What does "with replacement" mean in GRE word problems?

"With replacement" means that after an item is selected, it is put back into the group before the next selection is made, keeping the total count and probabilities the same for each draw. For more practice on these terms, check out our GRE Reading Practice Test to improve your word problem comprehension.

What is the complement of an event?

The complement of an event is the probability that the event does not happen, calculated as 1 minus the probability of the event. It is a useful shortcut for problems asking for "at least one" or "not" a specific outcome.

Are calculators allowed for probability questions on the GRE?

Yes, the GRE provides an on-screen calculator for the Quantitative Reasoning section, which you can use to divide fractions into decimals if needed. However, most easy probability problems are faster to solve using simple fraction reduction.