In this post, you will come across all the possible probability questions that are likely to show up on the GRE exam.
Questions
Question 1
A certain box contains 20 marbles — 4 black, 8 brown, 6 silver, and 2 red. If a marble is to be chosen at random, what is the probability that the marble will be neither silver nor brown?
(A) 1/50
(B) 3/15
(C) 3/10
(D) 7/10
(E) 13/10
Question 2
Of the 50 students in a certain class, 5 speak French. Two students of the class will be selected at random. Which of the following is closest to the probability that neither of the students selected will speak French?
(A) 0.01
(B) 0.15
(C) 0.72
(D) 0.81
(E) 0.99
Question 3
x is the probability that event A will occur, and y is the probability that event A will not occur.
Quantity A: x + y
Quantity B: xy
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Question 4
A random variable A is normally distributed with a mean of 50 and a standard deviation of 2.
Quantity A: The probability of the event that the value of A is smaller than 46
Quantity B: 1/10
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.
Question 5
Of the 10 marbles in a box, 2 are green. A person will select 2 marbles simultaneously and at random from the box. What is the probability that neither of the marbles selected will be green?
(A) 16/90
(B) 56/90
(C) 64/100
(D) 96/100
(E) 88/90
Question 6
In an experiment, A and B are independent events. The probability that event A will happen is a, and the probability that event B will happen is b, where both a and b are greater than 0. What is the probability that event A will happen or event B will happen but not both?
* An independent event is an event that has no connection to another event’s chances of happening (or not happening).
(A) a + b
(B) a + b – ab
(C) a + b – 2ab
(D) a + b + 2ab
(E) 1
Question 7
On a number line, there are 6 distinct points, of which 4 are positive and 2 are negative. If 2 different points are to be randomly selected, what is the probability that the 2 points selected will both be positive?
(A) 2/5
(B) 4/9
(C) 3/5
(D) 8/9
(E) 14/15
Question 8
Of the 20 employees in a company, 5 have an MBA. If 3 employees are to be simultaneously selected at random, which of the following represents the probability that only 1 of the 3 employees selected will have an MBA? (Give your answer as a fraction)
Question 9
The diagram above shows the probability distribution of a variable Y. For each of the ranges shown, the diagram gives the probability that the value of Y is in that range. What is the probability that -1 < Y < 2? (Give your answer to 2 decimal places)
Question 10
Suppose that there is a coin that is weighted in such a way that each time the coin is tossed, the probability of tossing head is twice the probability of tossing a tail. What is the probability of tossing a head?
(A) 1/3
(B) 1/2
(C) 3/5
(D) 2/3
(E) 4/5
Question 11
Suppose that there is a 6-sided die with faces numbered 1 through 6. This die is rolled twice. What is the probability that the first roll will be an odd number and the second roll will be an even number?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 5/6
(E) 1
Question 12
A certain event has only four possible outcomes. The probabilities of each outcome is a, b, c, and d, respectively. If a = 1 – 3d, what is a in terms of b and c?
A) b + c
B) (4b + c)/3
C) 1 – 3(b + c)/2
D) (1 + 2c)/2
E) 2 – (3b – c)/2
Question 13
Forty-five marbles are numbered consecutively from 1 through 45. If one marble is to be drawn at random, what is the probability that the number on the selected marble will be a multiple of 5 or a multiple of 7 or a multiple of both 5 and 7 ?
A) 9/45
B) 11/45
C) 13/45
D) 14/45
E) 15/45
Question 14
The ratio of the probability of event X occuring to the probability of X not occuring is 5 to 9. What is the probability that event X will not occur?
A) 3/14
B) 5/14
C) 4/9
D) 5/9
E) 9/14
Question 15
In a set of positive integers greater than 1, the ratio of the number of prime numbers to the number of composite numbers is 3 to 7. If one number is selected at random, what is the probability that it will not be a composite number?
A) 3/10
B) 4/10
C) 6/10
D) 7/10
E) Cannot be determined from the given information.
Question 16
For a certain probabilistic experiment, events A and B are mutually exclusive. The probability that the event A U B (that is, the event A or B, or both) will occur is 0.6. Given that the probability of event A is 0.2, what is the probability of event B?
Question 17
For a certain probabilistic experiment, events X and Y are independent. The probability P (X or Y) is 0.6. Given that probability P (X) = 0.5, what if the probability P (Y)?
Question 18
In a probability experiment, the probability of W happening is 60% and the probability of Z happening is 35%. What could be the probability of the event W or Z, or both happening?
Indicate all that apply.
A) 30%
B) 35%
C) 60%
D) 70%
E) 95%
F) 97%
G) 100%
Question 19
For a certain probabilistic experiment, events X and Y are independent. The probability of X occurring is 0.8 and the probability of Y happening is 0.7. What is the probability that both X and Y will happen?
Question 20
The probability that Andrew will score a 320 on the GRE is 0.3. The probability that Bill will score a 320 on the GRE is 0.4.
Quantity A: Probability that at least one of them will score a 320
Quantity B: Probability that none of them will score a 320
(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.