GRE Probability and Statistics Concepts 3 — Questions and Answers
Question 1: A coin is flipped 3 times. What is the probability of getting exactly two heads?
- 1/8
- 3/8 (Correct answer)
- 1/2
- 1/4
Correct answer: 3/8
There are 3 favorable arrangements (HHT, HTH, THH) out of 8 outcomes, giving 3/8.
Question 2: The standard deviation measures which characteristic of a data set?
- Central tendency
- Spread around the mean (Correct answer)
- The most frequent value
- The range only
Correct answer: Spread around the mean
Standard deviation quantifies how dispersed the values are around the mean.
Question 3: How many distinct ways can 4 different books be arranged on a shelf?
- 12
- 16
- 24 (Correct answer)
- 36
Correct answer: 24
The number of arrangements is 4! = 24.
Question 4: If a card is drawn from a standard 52-card deck, what is the probability it is a face card (J, Q, K)?
- 3/13 (Correct answer)
- 1/13
- 1/4
- 4/13
Correct answer: 3/13
There are 12 face cards out of 52, giving 12/52 = 3/13.
Question 5: What is the mode of the data set {2, 4, 4, 6, 6, 6, 9}?
- 4
- 6 (Correct answer)
- 5
- 9
Correct answer: 6
The value 6 appears three times, more than any other, so it is the mode.
Question 6: Two dice are rolled. What is the probability that at least one shows a 6?
- 11/36 (Correct answer)
- 1/6
- 1/3
- 10/36
Correct answer: 11/36
P(at least one 6) = 1 − (5/6)² = 1 − 25/36 = 11/36.
Question 7: In how many ways can a committee of 2 be chosen from 5 people?
- 10 (Correct answer)
- 20
- 25
- 5
Correct answer: 10
Order does not matter, so C(5,2) = 10.
GRE Probability and Statistics Concepts 3
A coin is flipped 3 times.
What is the probability of getting exactly two heads?