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Probability and Statistics Concepts Flashcards

6 cards from real GRE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  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?

    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.

  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?

    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.

  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?

    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.

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

    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.

  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?

    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.

  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?

    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.