Explore essential probability and statistics concepts commonly tested on the GRE. This quiz is designed to help students strengthen their understanding of key ideas like distributions, expected value, sample spaces, and more—all critical for mastering GRE quantitative reasoning.
If a fair six-sided die is rolled once, what is the probability of rolling a number greater than 4?
Explanation: There are two outcomes greater than 4 (rolling a 5 or 6) out of a total of six possible outcomes, so the probability is 2/6, which simplifies to 1/3. Option 1/2 is incorrect as it would be the case if there were three successful outcomes. The answer 2/3 is incorrect because it overestimates the favourable outcomes, and 1/6 corresponds to just one successful outcome, not two.
Given the data set: 4, 7, 7, 8, 10, what is the median of this set?
Explanation: To find the median, arrange the numbers in order (already done). With five data points, the middle value is the third, which is 7. The option 8 is incorrect, as it's the fourth value. Options 4 and 10 represent the extremes (minimum and maximum) but do not reflect the central value of this odd-sized dataset.
A bag contains 3 red marbles and 2 blue marbles. If a single marble is chosen at random, what is the expected number of red marbles drawn?
Explanation: The probability of drawing a red marble is 3 out of 5, so the expected value for one draw is (3/5) × 1 + (2/5) × 0 = 0.6. Options 1.5, 3, and 2 are either the sum or counts of marbles, not the expected probability for a single draw. Only 0.6 correctly represents the average red marbles drawn in a single trial.
Which sampling method ensures each member of a population has an equal chance of being chosen, such as drawing names from a hat?
Explanation: Simple random sampling gives every individual in a population an equal chance of selection, like drawing names from a hat. Stratified sampling divides the population into groups and samples from each, cluster sampling selects entire groups, and systematic sampling picks every nth individual, so none of these guarantee individual equality like simple random sampling.
What best describes the standard deviation of a data set?
Explanation: Standard deviation quantifies how much the values in a data set deviate from the mean, making it a measure of spread. The median is the middle value, not a measure of spread. The range is the largest minus the smallest value. Standard deviation is not related to probability between events, making the latter distractor incorrect.