Expected value and probability distributions worksheet for Statistics

Statistics treats expected value as the mean of a discrete random variable, the long-run average over many trials. Check first that the probabilities add to 1, then weight each outcome by its probability. Games, raffles and insurance policies are judged by whether that mean is positive, negative or zero, and zero is a fair game.

Also taught in Algebra 2 and Precalculus, each at its own level and with its own examples.

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Sigma Prep · sigmaprep.io/worksheets Name Expected Value and Probability Distributions Date Period Answer each question. Find the expected value from a table $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 13 & 6 & - 2 & 1 \\ P (x) & \frac{1}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{2} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 1 & - 5 & - 2 & 10 \\ P (x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 7 & - 1 & - 4 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 17 & - 2 & 10 & 11 \\ P (x) & \frac{5}{16} & \frac{1}{16} & \frac{9}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 1 & 15 & 18 & 2 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ Find the expected profit or fair price A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 15.48$ with probability $\frac{1}{6}$ , or nothing; the $$ 4.00$ is not given back. What price for one throw would make the expected profit zero? A game costs $$ 5.00$ to play. It pays out a prize of $$ 13.20$ with probability $\frac{1}{2}$ , and otherwise nothing; the $$ 5.00$ is not returned. Someone pays for $20$ plays. Find their expected total profit. A raffle ticket costs $$ 5.00$ . It wins a prize of $$ 15.68$ with probability $\frac{1}{8}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 34.40$ with probability $\frac{7}{20}$ and a prize of $$ 3.40$ with probability $\frac{1}{4}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? A scratch card sells for $$ 4.00$ . It pays out a prize of $$ 25.00$ with probability $\frac{1}{2}$ ; the $$ 4.00$ is not refunded. Someone pays for $25$ cards. Find their expected total profit. Find the missing probability $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{4} & \frac{7}{16} & \frac{3}{16} & ? \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{12} & \frac{1}{6} & ? & \frac{5}{12} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{12} & \frac{1}{6} & \frac{7}{12} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{16} & ? & \frac{7}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{6} & \frac{1}{6} & \frac{1}{12} \end{array} \end{aligned}$ Find the mean and standard deviation A bag holds 10 tickets: 2 marked 0, 3 marked 10, 1 marked 20 and 4 marked 30. One ticket is drawn at random, and $X$ is the number on it. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. Let $X$ be the change in a stock price, in dollars, over one day. One probability is missing from the table. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & ? & 0.4 & 0.3 \end{array}$ Let $X$ be the number of goals a team scores in a game. It takes the values 0, 1, 2 and 3 with probabilities 0.3, 0.1, 0.3 and 0.3, in that order. Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. Let $X$ be the number of tries a student needs to pass a driving test. Give the expected value and the standard deviation of $X$ , each to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.4 & 0.4 & 0.1 & 0.1 \end{array}$ Let $X$ be the number of books a student borrows on a library visit. One probability is missing from the table. Find its expected value $μ$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.1 & 0.1 & 0.3 & ? \end{array}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Expected Value and Probability Distributions

Date Period

Answer each question.

Find the expected value from a table
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 13 & 6 & - 2 & 1 \\ P (x) & \frac{1}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{2} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 1 & - 5 & - 2 & 10 \\ P (x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 7 & - 1 & - 4 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 17 & - 2 & 10 & 11 \\ P (x) & \frac{5}{16} & \frac{1}{16} & \frac{9}{16} & \frac{1}{16} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 1 & 15 & 18 & 2 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$

Find the expected profit or fair price
A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 15.48$ with probability $\frac{1}{6}$ , or nothing; the $$ 4.00$ is not given back. What price for one throw would make the expected profit zero?
A game costs $$ 5.00$ to play. It pays out a prize of $$ 13.20$ with probability $\frac{1}{2}$ , and otherwise nothing; the $$ 5.00$ is not returned. Someone pays for $20$ plays. Find their expected total profit.
A raffle ticket costs $$ 5.00$ . It wins a prize of $$ 15.68$ with probability $\frac{1}{8}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player.
A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 34.40$ with probability $\frac{7}{20}$ and a prize of $$ 3.40$ with probability $\frac{1}{4}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero?
A scratch card sells for $$ 4.00$ . It pays out a prize of $$ 25.00$ with probability $\frac{1}{2}$ ; the $$ 4.00$ is not refunded. Someone pays for $25$ cards. Find their expected total profit.

Find the missing probability
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{4} & \frac{7}{16} & \frac{3}{16} & ? \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{12} & \frac{1}{6} & ? & \frac{5}{12} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{12} & \frac{1}{6} & \frac{7}{12} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{16} & ? & \frac{7}{16} & \frac{1}{16} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{6} & \frac{1}{6} & \frac{1}{12} \end{array} \end{aligned}$

Find the mean and standard deviation
A bag holds 10 tickets: 2 marked 0, 3 marked 10, 1 marked 20 and 4 marked 30. One ticket is drawn at random, and $X$ is the number on it. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth.
Let $X$ be the change in a stock price, in dollars, over one day. One probability is missing from the table. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & ? & 0.4 & 0.3 \end{array}$
Let $X$ be the number of goals a team scores in a game. It takes the values 0, 1, 2 and 3 with probabilities 0.3, 0.1, 0.3 and 0.3, in that order. Work out $μ$ and $σ$ for $X$ , to the nearest hundredth.
Let $X$ be the number of tries a student needs to pass a driving test. Give the expected value and the standard deviation of $X$ , each to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.4 & 0.4 & 0.1 & 0.1 \end{array}$
Let $X$ be the number of books a student borrows on a library visit. One probability is missing from the table. Find its expected value $μ$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.1 & 0.1 & 0.3 & ? \end{array}$



Sigma Prep · sigmaprep.io/worksheets Name Expected Value and Probability DistributionsAnswer keyVersion 3 Date Period Answer each question. Find the expected value from a table $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 13 & 6 & - 2 & 1 \\ P (x) & \frac{1}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{2} \end{array} \end{aligned}$ $\frac{55}{16}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 1 & - 5 & - 2 & 10 \\ P (x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{7}{4}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 7 & - 1 & - 4 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{13}{8}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 17 & - 2 & 10 & 11 \\ P (x) & \frac{5}{16} & \frac{1}{16} & \frac{9}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\frac{23}{2}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 1 & 15 & 18 & 2 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $5$ Find the expected profit or fair price A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 15.48$ with probability $\frac{1}{6}$ , or nothing; the $$ 4.00$ is not given back. What price for one throw would make the expected profit zero? $$ 2.58$ A game costs $$ 5.00$ to play. It pays out a prize of $$ 13.20$ with probability $\frac{1}{2}$ , and otherwise nothing; the $$ 5.00$ is not returned. Someone pays for $20$ plays. Find their expected total profit. $$ 32.00$ A raffle ticket costs $$ 5.00$ . It wins a prize of $$ 15.68$ with probability $\frac{1}{8}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. $- $ 3.04$ A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 34.40$ with probability $\frac{7}{20}$ and a prize of $$ 3.40$ with probability $\frac{1}{4}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? $$ 12.89$ A scratch card sells for $$ 4.00$ . It pays out a prize of $$ 25.00$ with probability $\frac{1}{2}$ ; the $$ 4.00$ is not refunded. Someone pays for $25$ cards. Find their expected total profit. $$ 212.50$ Find the missing probability $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{4} & \frac{7}{16} & \frac{3}{16} & ? \end{array} \end{aligned}$ $\frac{1}{8}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{12} & \frac{1}{6} & ? & \frac{5}{12} \end{array} \end{aligned}$ $\frac{1}{3}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{12} & \frac{1}{6} & \frac{7}{12} \end{array} \end{aligned}$ $\frac{1}{6}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{16} & ? & \frac{7}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\frac{7}{16}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{6} & \frac{1}{6} & \frac{1}{12} \end{array} \end{aligned}$ $\frac{7}{12}$ Find the mean and standard deviation A bag holds 10 tickets: 2 marked 0, 3 marked 10, 1 marked 20 and 4 marked 30. One ticket is drawn at random, and $X$ is the number on it. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $μ = 17$ , $σ \approx 11.87$ Let $X$ be the change in a stock price, in dollars, over one day. One probability is missing from the table. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & ? & 0.4 & 0.3 \end{array}$ $μ = - 0.1$ , $σ \approx 0.94$ Let $X$ be the number of goals a team scores in a game. It takes the values 0, 1, 2 and 3 with probabilities 0.3, 0.1, 0.3 and 0.3, in that order. Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $μ = 1.6$ , $σ \approx 1.20$ Let $X$ be the number of tries a student needs to pass a driving test. Give the expected value and the standard deviation of $X$ , each to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.4 & 0.4 & 0.1 & 0.1 \end{array}$ $μ = 1.9$ , $σ \approx 0.94$ Let $X$ be the number of books a student borrows on a library visit. One probability is missing from the table. Find its expected value $μ$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.1 & 0.1 & 0.3 & ? \end{array}$ $μ = 3.2$ , $σ \approx 0.98$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Expected Value and Probability DistributionsAnswer keyVersion 3

Date Period

Answer each question.

Find the expected value from a table
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 13 & 6 & - 2 & 1 \\ P (x) & \frac{1}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{2} \end{array} \end{aligned}$ $\frac{55}{16}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 1 & - 5 & - 2 & 10 \\ P (x) & \frac{1}{4} & \frac{1}{2} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{7}{4}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 7 & - 1 & - 4 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{13}{8}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 17 & - 2 & 10 & 11 \\ P (x) & \frac{5}{16} & \frac{1}{16} & \frac{9}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\frac{23}{2}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 1 & 15 & 18 & 2 \\ P (x) & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $5$

Find the expected profit or fair price
A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 15.48$ with probability $\frac{1}{6}$ , or nothing; the $$ 4.00$ is not given back. What price for one throw would make the expected profit zero? $$ 2.58$
A game costs $$ 5.00$ to play. It pays out a prize of $$ 13.20$ with probability $\frac{1}{2}$ , and otherwise nothing; the $$ 5.00$ is not returned. Someone pays for $20$ plays. Find their expected total profit. $$ 32.00$
A raffle ticket costs $$ 5.00$ . It wins a prize of $$ 15.68$ with probability $\frac{1}{8}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. $- $ 3.04$
A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 34.40$ with probability $\frac{7}{20}$ and a prize of $$ 3.40$ with probability $\frac{1}{4}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? $$ 12.89$
A scratch card sells for $$ 4.00$ . It pays out a prize of $$ 25.00$ with probability $\frac{1}{2}$ ; the $$ 4.00$ is not refunded. Someone pays for $25$ cards. Find their expected total profit. $$ 212.50$

Find the missing probability
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{4} & \frac{7}{16} & \frac{3}{16} & ? \end{array} \end{aligned}$ $\frac{1}{8}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{12} & \frac{1}{6} & ? & \frac{5}{12} \end{array} \end{aligned}$ $\frac{1}{3}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{12} & \frac{1}{6} & \frac{7}{12} \end{array} \end{aligned}$ $\frac{1}{6}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{16} & ? & \frac{7}{16} & \frac{1}{16} \end{array} \end{aligned}$ $\frac{7}{16}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{6} & \frac{1}{6} & \frac{1}{12} \end{array} \end{aligned}$ $\frac{7}{12}$

Find the mean and standard deviation
A bag holds 10 tickets: 2 marked 0, 3 marked 10, 1 marked 20 and 4 marked 30. One ticket is drawn at random, and $X$ is the number on it. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $μ = 17$ , $σ \approx 11.87$
Let $X$ be the change in a stock price, in dollars, over one day. One probability is missing from the table. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & ? & 0.4 & 0.3 \end{array}$ $μ = - 0.1$ , $σ \approx 0.94$
Let $X$ be the number of goals a team scores in a game. It takes the values 0, 1, 2 and 3 with probabilities 0.3, 0.1, 0.3 and 0.3, in that order. Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $μ = 1.6$ , $σ \approx 1.20$
Let $X$ be the number of tries a student needs to pass a driving test. Give the expected value and the standard deviation of $X$ , each to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.4 & 0.4 & 0.1 & 0.1 \end{array}$ $μ = 1.9$ , $σ \approx 0.94$
Let $X$ be the number of books a student borrows on a library visit. One probability is missing from the table. Find its expected value $μ$ and its standard deviation $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ P (x) & 0.1 & 0.1 & 0.3 & ? \end{array}$ $μ = 3.2$ , $σ \approx 0.98$

How to do these

An insurer charges $$ 300$ for a policy that pays $$ 20,000$ with probability $0.01$ . Find the insurer's expected profit

Expected payout: 20000 × 0.01 = 200.
Profit is the premium minus the expected payout: 300 - 200.

The answer is $$ 100.00$ .

Where students go wrong

Subtracting the cost twice. If a ticket costs $5 and pays $50, either use a net gain of $45 on a win and -$5 on a loss, or subtract $5 once from the expected payout, but not both.

Also called probability distributions, expected payoff, fair games or discrete random variables.

What you can put on this worksheet

Expected value from a table: Find the expected value.
$\begin{array}{cccc} x & 1 & 3 & 4 \\ P (x) & \frac{2}{5} & \frac{2}{5} & \frac{1}{5} \end{array}$ → $\frac{12}{5}$
Expected profit of a game: A scratch card sells for $$ 2.00$ . It pays out a prize of $$ 2.40$ with probability $\frac{2}{5}$ ; the $$ 2.00$ is not refunded. Find the expected prize money per card, before the price is taken off. → $$ 0.96$
The missing probability: Find the missing probability.
$\begin{array}{cccc} outcome & A & B & C \\ P & ? & \frac{2}{5} & \frac{1}{5} \end{array}$ → $\frac{2}{5}$
Mean and standard deviation: A bag holds 10 tickets: 2 marked 0, 5 marked 10 and 3 marked 20. One ticket is drawn at random, and $X$ is the number on it. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. → $μ = 11$ , $σ \approx 7.00$

Questions about these worksheets

Yes. Every expected value and probability distributions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the expected value and probability distributions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 4: expected value from a table, expected profit of a game, the missing probability and mean and standard deviation. Tick as many as you want and set how many of each, or let it spread them evenly.

Forgetting the cost, or forgetting that the probabilities have to add to 1 before a missing one can be found.

Expected value and probability distributions worksheet for Statistics

Select your difficulty

Find the expected value from a table

Find the expected profit or fair price

Find the missing probability

Find the mean and standard deviation

Find the expected value from a table

Find the expected profit or fair price

Find the missing probability

Find the mean and standard deviation

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these expected value and probability distributions worksheets free?+

Do the expected value and probability distributions worksheets come with an answer key?+

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Is this a free alternative to Kuta Software for expected value and probability distributions?+

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What do students get wrong with expected value and probability distributions?+