Easy GRE Probability Practice Test Practice Questions

Concept Explanation

Probability measures the likelihood that a specific event will occur, expressed as a numerical value between 0 and 1. In the context of an Easy GRE Probability Practice Test, most problems focus on the fundamental formula where the probability of an event $P(E)$ is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in the sample space.

To excel in this section of the GRE Prep, you must understand three core rules. First, the probability of an event that is certain to happen is 1, while the probability of an impossible event is 0. Second, the sum of the probabilities of all possible mutually exclusive outcomes must equal 1. This leads to the concept of the complement: the probability of an event NOT happening is $1 - P( \text{Event})$. Third, for independent events—where the outcome of one does not affect the other—the probability of both occurring is found by multiplying their individual probabilities.

Basic probability questions often involve standard objects like fair six-sided dice, decks of 52 cards, or jars containing colored marbles. Understanding how to count these outcomes is essential. For more comprehensive review, you might explore Free GRE Practice Questions Practice Questions with Answers to see how probability interacts with other quantitative topics.

Solved Examples

1. Single Event: A jar contains 4 red marbles, 5 blue marbles, and 11 green marbles. If one marble is selected at random, what is the probability that it is blue?
   1. Identify the number of favorable outcomes: There are 5 blue marbles.
   2. Calculate the total number of outcomes: $4 + 5 + 11 = 20$.
   3. Apply the formula: $P( \text{blue}) = \frac{5}{20}$.
   4. Simplify the fraction: $\frac{1}{4}$ or 0.25.
2. Independent Events: A fair coin is flipped twice. What is the probability that it lands on heads both times?
   1. Determine the probability of heads on the first flip: $P(H_1) = \frac{1}{2}$.
   2. Determine the probability of heads on the second flip: $P(H_2) = \frac{1}{2}$.
   3. Since the flips are independent, multiply the probabilities: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.
   4. The final probability is 0.25.
3. Complementary Events: The probability that it will rain tomorrow is $\frac{3}{10}$. What is the probability that it will NOT rain tomorrow?
   1. Identify the probability of the event: $P( \text{rain}) = 0.3$.
   2. Use the complement rule: $P( \text{not rain}) = 1 - P( \text{rain})$.
   3. Calculate: $1 - 0.3 = 0.7$.
   4. The result is $\frac{7}{10}$.

Practice Questions

1. A bag contains 6 black pens and 14 blue pens. If one pen is chosen at random, what is the probability that the pen is black?
2. A standard six-sided die is rolled once. What is the probability of rolling a number greater than 4?
3. In a group of 50 students, 20 are enrolled in Biology, 25 are enrolled in Chemistry, and 5 are enrolled in both. If a student is chosen at random, what is the probability they are enrolled in at least one of these two subjects?

4. If the probability of an event occurring is $\frac{2}{7}$, what is the probability of the event not occurring?
5. Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 3?
6. A drawer contains 10 white socks and 10 black socks. If you pick one sock at random, what is the probability it is white?
7. A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability that the spinner lands on a prime number?
8. Box A contains 3 red balls and 2 white balls. Box B contains 4 red balls and 6 white balls. If one ball is drawn from each box, what is the probability that both balls are red?
9. A letter is chosen at random from the word "PROBABILITY". What is the probability that the letter is a vowel (A, E, I, O, U)?
10. The probability that a target is hit by a single shot is 0.6. If two independent shots are fired, what is the probability that both shots miss the target?

Answers & Explanations

1. Answer: $\frac{3}{10}$ or 0.3. There are 6 black pens out of a total of 20 ($6 + 14$). The probability is $\frac{6}{20}$, which simplifies to $\frac{3}{10}$.
2. Answer: $\frac{1}{3}$. The numbers greater than 4 on a die are 5 and 6 (2 outcomes). The total outcomes are 6. Probability = $\frac{2}{6} = \frac{1}{3}$.
3. Answer: 0.8 or $\frac{4}{5}$. Use the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Here, $\frac{20}{50} + \frac{25}{50} - \frac{5}{50} = \frac{40}{50} = 0.8$.
4. Answer: $\frac{5}{7}$. The sum of an event and its complement is 1. $1 - \frac{2}{7} = \frac{5}{7}$.
5. Answer: $\frac{1}{18}$. The total possible outcomes for two dice are $6 \times 6 = 36$. The pairs that sum to 3 are (1,2) and (2,1). Probability = $\frac{2}{36} = \frac{1}{18}$.
6. Answer: 0.5. There are 10 white socks out of 20 total socks. $\frac{10}{20} = 0.5$.
7. Answer: 0.5. The prime numbers between 1 and 8 are 2, 3, 5, and 7 (4 numbers). Total outcomes are 8. $\frac{4}{8} = 0.5$.
8. Answer: 0.24 or $\frac{6}{25}$. Probability of red from Box A is $\frac{3}{5}$. Probability of red from Box B is $\frac{4}{10}$. Multiply them: $\frac{3}{5} \times \frac{4}{10} = \frac{12}{50} = 0.24$.
9. Answer: $\frac{4}{11}$. The word "PROBABILITY" has 11 letters. The vowels are O, A, I, I (4 vowels). Probability = $\frac{4}{11}$.
10. Answer: 0.16. The probability of missing a single shot is $1 - 0.6 = 0.4$. For two independent shots to miss, multiply: $0.4 \times 0.4 = 0.16$. For more practice with complex scenarios, try our AI Exam Simulator.

1. If a card is drawn from a standard deck of 52 cards, what is the probability it is an Ace?

• A1/52
• B1/13
• C1/4
• D4/13

Frequently Asked Questions

What is the range of probability values on the GRE?

Probability values on the GRE always range from 0 to 1. A value of 0 indicates an impossible event, while a value of 1 indicates an event that is certain to occur.

How do I identify independent events in GRE word problems?

Events are independent if the outcome of the first event does not change the likelihood of the second event. Common examples include rolling dice twice or drawing marbles with replacement.

What does "mutually exclusive" mean in probability?

Mutually exclusive events are events that cannot happen at the same time. For example, a single coin flip cannot result in both heads and tails simultaneously.

How do I calculate the probability of multiple independent events?

To find the probability that multiple independent events all happen, you multiply the individual probability of each event together. This is often referred to as the multiplication rule.

What is the difference between probability and odds?

Probability is the ratio of favorable outcomes to total outcomes, whereas odds is the ratio of favorable outcomes to unfavorable outcomes. The GRE primarily tests probability.