GRE - Graduate Record Examinations Probability and Statistics Concepts Questions and Answers 1 — 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?

4/15
11/15 (Correct answer)
1/3
2/3

Correct answer: 11/15

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?

336
24
56 (Correct answer)
120

Correct answer: 56

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?

11
8
7
9 (Correct answer)

Correct answer: 9

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?

{5, 15, 25, 35, 45}
{24, 25, 25, 25, 26} (Correct answer)
{0, 0, 25, 50, 50}
{20, 20, 20, 30, 30}

Correct answer: {24, 25, 25, 25, 26}

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?

1/78 (Correct answer)
1/13
1/6
2/39

Correct answer: 1/78

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.

Question 6: In a group of 200 students, 100 play a sport, 80 are in a club, and 30 both play a sport and are in a club. What is the probability that a student chosen at random plays a sport OR is in a club?

9/10
1/2
2/5
3/4 (Correct answer)

Correct answer: 3/4

To find the probability of event A or event B occurring, we use the formula: P(A or B) = P(A) + P(B) - P(A and B). Here, A is playing a sport and B is being in a club. P(A) = 100/200 = 1/2. P(B) = 80/200 = 2/5. P(A and B) = 30/200 = 3/20. So, P(A or B) = (100/200) + (80/200) - (30/200) = 150/200, which simplifies to 3/4.

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