GRE - Graduate Record Examinations Probability and Statistics Concepts Questions and Answers

Question 1

A bag contains 6 red, 4 blue, and 5 green marbles. If one marble is drawn at random, what is the probability that the marble is NOT blue?

Accepted Answer

11/15

Answer

The total number of marbles is 6 (red) + 4 (blue) + 5 (green) = 15. The number of marbles that are not blue is 6 (red) + 5 (green) = 11. The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of drawing a marble that is not blue is 11/15.

Question 2

A company with 8 junior developers needs to form a team of 3 to send to a conference. How many different teams of 3 can be formed?

Accepted Answer

56

Answer

This is a combination problem because the order in which the developers are chosen for the team does not matter. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items to choose from, and r is the number of items to choose. Here, n=8 and r=3. So, 8C3 = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 336 / 6 = 56.

Question 3

The mean (arithmetic mean) of the five numbers {7, 3, 11, x, 15} is 9. What is the median of this set of numbers?

Accepted Answer

9

Answer

The mean is the sum of the numbers divided by the count of the numbers. The sum is 7 + 3 + 11 + x + 15 = 36 + x. The count is 5. So, (36 + x) / 5 = 9. Multiplying both sides by 5 gives 36 + x = 45. Solving for x gives x = 9. Now, arrange the set of numbers in ascending order: {3, 7, 9, 11, 15}. The median is the middle number in an ordered set. In this case, the median is 9.

Question 4

Which of the following sets of numbers has the smallest standard deviation?

Accepted Answer

{24, 25, 25, 25, 26}

Answer

Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. The set {24, 25, 25, 25, 26} has its values most tightly clustered around its mean (which is 25). The other sets have values that are more spread out. The GRE expects a conceptual understanding of standard deviation rather than a full calculation.

Question 5

A standard six-sided die is rolled and a card is drawn from a standard 52-card deck. What is the probability of rolling a 4 and drawing a Jack?

Accepted Answer

1/78

Answer

These are two independent events, meaning the outcome of one does not affect the outcome of the other. The probability of rolling a 4 on a six-sided die is 1/6. The probability of drawing a Jack from a 52-card deck is 4/52 (since there are 4 Jacks), which simplifies to 1/13. To find the probability of both independent events occurring, we multiply their individual probabilities: P(A and B) = P(A) * P(B). So, (1/6) * (1/13) = 1/78.

GRE Practice Test

GRE Practice Test

GRE - Graduate Record Examinations Probability and Statistics Concepts Questions and Answers