Easy GRE Probability Set 2 Practice Questions

Probability measures the likelihood of a specific event occurring, expressed as a ratio between 0 and 1. While the quantitative section of the Graduate Record Examination (GRE) can feel intimidating, the foundation of Easy GRE Probability Set 2 Practice Questions relies on simple counting and basic arithmetic. Understanding how to calculate the chance of drawing a specific card or rolling a particular sum on dice is essential for scoring well on the GRE Prep journey. These concepts are not just academic; they represent the same logic used in risk assessment and statistical modeling across various professional fields.

Concept Explanation

Probability is the mathematical study of randomness, defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in a sample space. To calculate the probability of an event $E$, denoted as $P(E)$, you use the following formula:

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

For the GRE, you must be comfortable with three primary rules of probability:

• The Range Rule: Every probability must fall between 0 and 1, inclusive. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain.
• The Complement Rule: The probability that an event will not occur is $1 - P(E)$. This is often useful when it is easier to calculate the chance of the event failing than the chance of it succeeding.
• Independent Events: If two events do not affect each other, the probability of both occurring is the product of their individual probabilities: $P(A \text{ and } B) = P(A) \times P(B)$.

Many students find that using an AI Question Generator helps them see these patterns across hundreds of variations, which is key for building intuition on the exam. You can find more structured practice in our GRE Practice Questions with Answers Practice Questions guide.

Solved Examples

Reviewing worked examples helps solidify the application of the probability formula before you attempt the practice set.

1. Example 1: Single Die Roll
   A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?
   Solution:
   1. Identify the total outcomes: {1, 2, 3, 4, 5, 6}. Total = 6.
   2. Identify favorable outcomes (greater than 4): {5, 6}. Favorable = 2.
   3. Apply the formula: $P = \frac{2}{6} = \frac{1}{3}$.
2. Example 2: Colored Marbles
   A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is picked at random, what is the probability it is NOT blue?
   Solution:
   1. Total marbles = $5 + 3 + 2 = 10$.
   2. Favorable outcomes (not blue) = Red + Green = $5 + 2 = 7$.
   3. Apply the formula: $P = \frac{7}{10} = 0.7$.
3. Example 3: Independent Events
   A coin is flipped and a standard 52-card deck is sampled for one card. What is the probability of getting heads and drawing an Ace?
   Solution:
   1. $P( \text{Heads}) = \frac{1}{2}$.
   2. $P( \text{Ace}) = \frac{4}{52} = \frac{1}{13}$.
   3. Multiply for both: $\frac{1}{2} \times \frac{1}{13} = \frac{1}{26}$.

Practice Questions

Test your skills with these Easy GRE Probability Set 2 Practice Questions. These are designed to mirror the level of difficulty found in the early stages of the GRE Quantitative section.

1. A box contains 8 light bulbs, 2 of which are defective. If one bulb is selected at random, what is the probability that it is NOT defective?
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. If a fair coin is flipped three times, what is the probability of getting exactly three tails?

4. A jar contains 12 black jelly beans and 18 white jelly beans. If one is chosen at random, what is the probability, expressed as a decimal, that it is black?
5. Two fair six-sided dice are rolled. What is the probability that the sum of the numbers shown is 3?
6. In a class of 30 students, 12 are wearing glasses. If a student is picked at random, what is the probability they are not wearing glasses?
7. A card is drawn from a standard 52-card deck. What is the probability that the card is a Heart or a Diamond?
8. If the probability of rain tomorrow is $0.35$, what is the probability that it will NOT rain tomorrow?
9. A bag has 4 red, 6 blue, and 10 yellow balls. What is the probability of drawing either a red or a blue ball?
10. If you roll a six-sided die, what is the probability of rolling a number that is a multiple of 3?

For more variety, check out GRE Practice Questions with Explanations Practice Questions or try our Adaptive GRE Practice Test Practice Questions.

Answers & Explanations

1. Answer: $\frac{3}{4}$ or 0.75
   Total bulbs = 8. Non-defective bulbs = $8 - 2 = 6$. Probability = $\frac{6}{8} = \frac{3}{4}$.
2. Answer: $\frac{1}{2}$ or 0.5
   Total numbers = 8. Prime numbers between 1 and 8 are {2, 3, 5, 7}. There are 4 primes. Probability = $\frac{4}{8} = \frac{1}{2}$.
3. Answer: $\frac{1}{8}$
   Each flip has a $\frac{1}{2}$ chance of tails. Since the flips are independent: $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$.
4. Answer: 0.4
   Total beans = $12 + 18 = 30$. Black beans = 12. Probability = $\frac{12}{30} = \frac{2}{5} = 0.4$.
5. Answer: $\frac{1}{18}$
   Total outcomes for two dice = $6 \times 6 = 36$. Sum of 3 occurs with (1,2) and (2,1). Total favorable = 2. Probability = $\frac{2}{36} = \frac{1}{18}$.
6. Answer: $\frac{3}{5}$ or 0.6
   Total students = 30. Not wearing glasses = $30 - 12 = 18$. Probability = $\frac{18}{30} = \frac{3}{5}$.
7. Answer: $\frac{1}{2}$ or 0.5
   There are 13 Hearts and 13 Diamonds in a deck of 52. Total favorable = 26. Probability = $\frac{26}{52} = \frac{1}{2}$.
8. Answer: 0.65
   Using the complement rule: $1 - 0.35 = 0.65$.
9. Answer: $\frac{1}{2}$ or 0.5
   Total balls = $4 + 6 + 10 = 20$. Red or blue = $4 + 6 = 10$. Probability = $\frac{10}{20} = \frac{1}{2}$.
10. Answer: $\frac{1}{3}$
    Outcomes for a die = {1, 2, 3, 4, 5, 6}. Multiples of 3 are {3, 6}. Probability = $\frac{2}{6} = \frac{1}{3}$.

Mastering these basics is a prerequisite for tackling more complex topics found in Unlimited GRE Practice Questions Practice Questions.

1. If a bag contains 4 green apples and 6 red apples, what is the probability of picking a green apple?

• A0.4
• B0.6
• C0.25
• D1.0

Frequently Asked Questions

What is the difference between independent and dependent events?

Independent events are those where the outcome of the first event does not change the probability of the second event, like flipping a coin twice. Dependent events occur when the first outcome changes the available options for the second, such as drawing cards from a deck without replacing them.

Can a probability ever be negative?

No, a probability cannot be negative because it represents a ratio of counts, and you cannot have a negative number of outcomes. The scale for probability strictly ranges from 0 to 1.

What does it mean if the probability of an event is 1?

A probability of 1 indicates that the event is certain to happen. In a sample space, this means every possible outcome satisfies the condition of the event.

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

To find the probability of both independent events occurring, you multiply the probability of the first event by the probability of the second event. This is known as the multiplication rule for independent events.

What is a sample space in probability?

The sample space is the set of all possible outcomes for a given experiment or random process. For example, the sample space for a standard die is {1, 2, 3, 4, 5, 6}.