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GRE Statistics and Probability — practice questions

Explore 171 free Statistics and Probability questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Statistics and Probability questions and exercises with answers

Showing questions 1–30 of 171.

Harpreet tosses two different coins simultaneously. What is the probability of getting at least one head?Read the answer and worked solution →Savita and Hamida are friends. Ignoring leap year, what is the probability that they have the same birthday?Read the answer and worked solution →One card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card is not an ace?Read the answer and worked solution →If $P(E)=0.62$, what is $P(\overline{E})$?Read the answer and worked solution →An event having only one outcome of an experiment is calledRead the answer and worked solution →What is the distance of the point $(-3,4)$ from the origin?Read the answer and worked solution →Batsman B scored 53, 46, 48, 50, 53, 53, 58, 60, 57, 52. What is the range?Read the answer and worked solution →The deviation of an observation $x$ from a fixed value $a$ is:Read the answer and worked solution →The sum of deviations of observations from their **mean** $\bar{x}$ is always:Read the answer and worked solution →Mean deviation about a value $a$ is calculated using:Read the answer and worked solution →The mean of the data $\{2, 4, 6, 8, 10\}$ is:Read the answer and worked solution →The median of $\{3, 5, 7, 9, 11\}$ is:Read the answer and worked solution →The median of $\{4, 6, 8, 10\}$ is:Read the answer and worked solution →The mode of $\{1, 2, 2, 3, 4, 4, 4, 5\}$ is:Read the answer and worked solution →The mean of batsman A's scores (30, 91, 0, 64, 42, 80, 30, 5, 117, 71) is:Read the answer and worked solution →The mean of batsman B's scores (53, 46, 48, 50, 53, 53, 58, 60, 57, 52) is:Read the answer and worked solution →The mean of the data $\{2, 3, 5, 7, 8\}$ is:Read the answer and worked solution →If all values in a data set are equal, the range is:Read the answer and worked solution →Which measure of dispersion depends on each observation (not just extremes)?Read the answer and worked solution →For the data $\{4, 4, 4, 4, 4\}$, the mean deviation about the mean is:Read the answer and worked solution →For the data $\{6, 7, 10, 12, 13, 4, 8, 12\}$, the mean is:Read the answer and worked solution →Karl Pearson, mentioned in your syllabus Statistics Ch 13, lived during which period?Read the answer and worked solution →Which of the following is true about the mean of deviations from the mean?Read the answer and worked solution →If the median of a data set is the same as its mean, the data distribution is:Read the answer and worked solution →In the formula $\bar{x} = \dfrac{1}{n} \sum x_i$, what does $n$ represent?Read the answer and worked solution →What does a 'measure of dispersion' tell us about a data set?Read the answer and worked solution →The probability of getting HEADS when flipping a fair coin is:Read the answer and worked solution →The probability of rolling a 3 on a fair six-sided die is:Read the answer and worked solution →What is the probability of rolling an EVEN number on a fair six-sided die?Read the answer and worked solution →A class of 30 students has 18 girls. The probability that a randomly chosen student is a BOY is:Read the answer and worked solution →

Worked practice questions

Harpreet tosses two different coins simultaneously. What is the probability of getting at least one head?

  1. $\frac{1}{4}$
  2. $\frac{1}{2}$
  3. $\frac{3}{4}$
  4. $1$
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Correct answer: C. $\frac{3}{4}$

The equally likely outcomes are $(H,H)$, $(H,T)$, $(T,H)$ and $(T,T)$. At least one head occurs in the first three outcomes, so there are 3 favourable outcomes out of 4. Thus the probability is $\frac{3}{4}$.

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Savita and Hamida are friends. Ignoring leap year, what is the probability that they have the same birthday?

  1. $\frac{1}{364}$
  2. $\frac{1}{365}$
  3. $\frac{364}{365}$
  4. $\frac{2}{365}$
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Correct answer: B. $\frac{1}{365}$

Fix Savita's birthday on any day. Hamida can have any of 365 equally likely birthdays, and only 1 of these matches Savita's. **So the probability of the same birthday is $\frac{1}{365}$.**

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One card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card is not an ace?

  1. $\frac{1}{13}$
  2. $\frac{4}{13}$
  3. $\frac{12}{13}$
  4. $\frac{48}{13}$
Show answer and solution

Correct answer: C. $\frac{12}{13}$

A deck has 4 aces, so non-aces are $52-4=48$. Hence the probability is $\frac{48}{52}=\frac{12}{13}$. Equivalently, it is $1-\frac{1}{13}=\frac{12}{13}$.

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More Mathematics topics

MathematicsArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits