GRE Probability and Statistics Concepts 2 — Questions and Answers
Question 1: A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls equals 7?
- 1/6 (Correct answer)
- 1/9
- 1/12
- 5/36
Correct answer: 1/6
There are 6 ordered pairs summing to 7 out of 36 equally likely outcomes, giving 6/36 = 1/6.
Question 2: If events A and B are independent with P(A) = 0.4 and P(B) = 0.5, what is P(A and B)?
- 0.9
- 0.2 (Correct answer)
- 0.1
- 0.45
Correct answer: 0.2
For independent events the joint probability is the product, 0.4 × 0.5 = 0.2.
Question 3: The mean of the data set {4, 8, 8, 10, 15} is closest to which value?
- 8
- 9 (Correct answer)
- 10
- 11
Correct answer: 9
The sum is 45 and there are 5 values, so the mean is 45/5 = 9.
Question 4: A bag has 3 red and 2 blue marbles. Two are drawn without replacement. What is the probability both are red?
- 3/10 (Correct answer)
- 9/25
- 2/5
- 1/5
Correct answer: 3/10
P = (3/5) × (2/4) = 6/20 = 3/10.
Question 5: What is the median of the set {12, 3, 7, 9, 15, 6}?
- 7
- 8 (Correct answer)
- 9
- 8.5
Correct answer: 8
Sorted, the middle two values are 7 and 9, so the median is (7+9)/2 = 8.
Question 6: In a standard normal distribution, approximately what percent of values fall within one standard deviation of the mean?
- 50%
- 68% (Correct answer)
- 95%
- 99.7%
Correct answer: 68%
The empirical rule states about 68% of data lies within one standard deviation of the mean.
Question 7: If P(A) = 0.7, what is the probability that A does NOT occur?
- 0.7
- 0.3 (Correct answer)
- 0.0
- 1.0
Correct answer: 0.3
The complement is 1 − 0.7 = 0.3.
GRE Probability and Statistics Concepts 2
A fair six-sided die is rolled twice.
What is the probability that the sum of the two rolls equals 7?