Expected value and probability distributions worksheet for Precalculus

Precalculus treats a probability distribution as a function from outcomes to probabilities and asks for both its mean and its standard deviation. The mean is the sum of x times P(x); the variance is the sum of x² times P(x) minus the mean squared, and the standard deviation is its square root.

Also taught in Algebra 2 and Statistics, 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 $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 16 & 10 & 6 & 3 \\ P (x) & \frac{5}{16} & \frac{3}{16} & \frac{1}{4} & \frac{1}{4} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & - 4 & 15 & 5 \\ P (x) & \frac{7}{12} & \frac{1}{4} & \frac{1}{12} & \frac{1}{12} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 6 & 3 & 10 \\ P (x) & \frac{7}{12} & \frac{1}{12} & \frac{1}{12} & \frac{1}{4} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 5 & 3 & - 2 & - 4 \\ P (x) & \frac{7}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{8} \end{array} \end{aligned}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & 11 & 0 & - 5 \\ P (x) & \frac{7}{16} & \frac{3}{16} & \frac{1}{8} & \frac{1}{4} \end{array} \end{aligned}$ Find the expected profit or fair price A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 10.86$ with probability $\frac{1}{2}$ , or nothing; the $$ 4.00$ is not given back. Someone pays for $25$ throws. Find their expected total profit. A game costs $$ 5.00$ to play. It pays out a prize of $$ 58.80$ with probability $\frac{1}{20}$ and a prize of $$ 9.00$ with probability $\frac{7}{20}$ , and otherwise nothing; the $$ 5.00$ is not returned. What should one play cost for the game to be fair? A raffle ticket costs $$ 4.00$ . It wins a prize of $$ 16.62$ with probability $\frac{1}{6}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 9.18$ with probability $\frac{1}{6}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? A scratch card sells for $$ 5.00$ . It pays out a prize of $$ 17.04$ with probability $\frac{1}{2}$ ; the $$ 5.00$ is not refunded. Someone pays for $10$ cards. Find their expected total profit. Find the missing probability $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{2}{3} & \frac{1}{6} & ? & \frac{1}{12} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & ? \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{2} & ? & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{6} & \frac{1}{3} & ? & \frac{1}{3} \end{array} \end{aligned}$ Find the mean and standard deviation Let $X$ be the net points won in one round of a game (a negative value is a loss). Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & 0.3 & 0.5 & 0.1 \end{array}$ Let $X$ be the prize, in dollars, won on a scratch card. One probability is missing from the table. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.3 & 0.4 & ? & 0.1 \end{array}$ Let $X$ be the number of calls a help desk gets in a minute. It takes the values 0, 1, 2 and 3 with probabilities 0.1, 0.2, 0.4 and 0.3, in that order. Find the mean and the standard deviation of $X$ , to the nearest hundredth. A spinner has 10 equal sections: 4 marked 1, 3 marked 2, 2 marked 3 and 1 marked 4. It is spun once, and $X$ is the number it lands on. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. Let $X$ be the points a team earns for one answer on a quiz show. One probability is missing from the table. Find $μ$ and $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.4 & 0.1 & ? & 0.1 \end{array}$ 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
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 16 & 10 & 6 & 3 \\ P (x) & \frac{5}{16} & \frac{3}{16} & \frac{1}{4} & \frac{1}{4} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & - 4 & 15 & 5 \\ P (x) & \frac{7}{12} & \frac{1}{4} & \frac{1}{12} & \frac{1}{12} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 6 & 3 & 10 \\ P (x) & \frac{7}{12} & \frac{1}{12} & \frac{1}{12} & \frac{1}{4} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 5 & 3 & - 2 & - 4 \\ P (x) & \frac{7}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{8} \end{array} \end{aligned}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & 11 & 0 & - 5 \\ P (x) & \frac{7}{16} & \frac{3}{16} & \frac{1}{8} & \frac{1}{4} \end{array} \end{aligned}$

Find the expected profit or fair price
A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 10.86$ with probability $\frac{1}{2}$ , or nothing; the $$ 4.00$ is not given back. Someone pays for $25$ throws. Find their expected total profit.
A game costs $$ 5.00$ to play. It pays out a prize of $$ 58.80$ with probability $\frac{1}{20}$ and a prize of $$ 9.00$ with probability $\frac{7}{20}$ , and otherwise nothing; the $$ 5.00$ is not returned. What should one play cost for the game to be fair?
A raffle ticket costs $$ 4.00$ . It wins a prize of $$ 16.62$ with probability $\frac{1}{6}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player.
A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 9.18$ with probability $\frac{1}{6}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero?
A scratch card sells for $$ 5.00$ . It pays out a prize of $$ 17.04$ with probability $\frac{1}{2}$ ; the $$ 5.00$ is not refunded. Someone pays for $10$ cards. Find their expected total profit.

Find the missing probability
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{2}{3} & \frac{1}{6} & ? & \frac{1}{12} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & ? \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{2} & ? & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{6} & \frac{1}{3} & ? & \frac{1}{3} \end{array} \end{aligned}$

Find the mean and standard deviation
Let $X$ be the net points won in one round of a game (a negative value is a loss). Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & 0.3 & 0.5 & 0.1 \end{array}$
Let $X$ be the prize, in dollars, won on a scratch card. One probability is missing from the table. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.3 & 0.4 & ? & 0.1 \end{array}$
Let $X$ be the number of calls a help desk gets in a minute. It takes the values 0, 1, 2 and 3 with probabilities 0.1, 0.2, 0.4 and 0.3, in that order. Find the mean and the standard deviation of $X$ , to the nearest hundredth.
A spinner has 10 equal sections: 4 marked 1, 3 marked 2, 2 marked 3 and 1 marked 4. It is spun once, and $X$ is the number it lands on. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth.
Let $X$ be the points a team earns for one answer on a quiz show. One probability is missing from the table. Find $μ$ and $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.4 & 0.1 & ? & 0.1 \end{array}$



Sigma Prep · sigmaprep.io/worksheets Name Expected Value and Probability DistributionsAnswer keyVersion 2 Date Period Answer each question. Find the expected value from a table $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 16 & 10 & 6 & 3 \\ P (x) & \frac{5}{16} & \frac{3}{16} & \frac{1}{4} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{73}{8}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & - 4 & 15 & 5 \\ P (x) & \frac{7}{12} & \frac{1}{4} & \frac{1}{12} & \frac{1}{12} \end{array} \end{aligned}$ $\frac{19}{4}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 6 & 3 & 10 \\ P (x) & \frac{7}{12} & \frac{1}{12} & \frac{1}{12} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{3}{2}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 5 & 3 & - 2 & - 4 \\ P (x) & \frac{7}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{27}{16}$ $\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & 11 & 0 & - 5 \\ P (x) & \frac{7}{16} & \frac{3}{16} & \frac{1}{8} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{31}{8}$ Find the expected profit or fair price A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 10.86$ with probability $\frac{1}{2}$ , or nothing; the $$ 4.00$ is not given back. Someone pays for $25$ throws. Find their expected total profit. $$ 35.75$ A game costs $$ 5.00$ to play. It pays out a prize of $$ 58.80$ with probability $\frac{1}{20}$ and a prize of $$ 9.00$ with probability $\frac{7}{20}$ , and otherwise nothing; the $$ 5.00$ is not returned. What should one play cost for the game to be fair? $$ 6.09$ A raffle ticket costs $$ 4.00$ . It wins a prize of $$ 16.62$ with probability $\frac{1}{6}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. $- $ 1.23$ A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 9.18$ with probability $\frac{1}{6}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? $$ 1.53$ A scratch card sells for $$ 5.00$ . It pays out a prize of $$ 17.04$ with probability $\frac{1}{2}$ ; the $$ 5.00$ is not refunded. Someone pays for $10$ cards. Find their expected total profit. $$ 35.20$ Find the missing probability $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} \end{array} \end{aligned}$ $\frac{1}{2}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{2}{3} & \frac{1}{6} & ? & \frac{1}{12} \end{array} \end{aligned}$ $\frac{1}{12}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & ? \end{array} \end{aligned}$ $\frac{1}{8}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{2} & ? & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $\frac{1}{4}$ $\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{6} & \frac{1}{3} & ? & \frac{1}{3} \end{array} \end{aligned}$ $\frac{1}{6}$ Find the mean and standard deviation Let $X$ be the net points won in one round of a game (a negative value is a loss). Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & 0.3 & 0.5 & 0.1 \end{array}$ $μ = - 0.4$ , $σ \approx 0.80$ Let $X$ be the prize, in dollars, won on a scratch card. One probability is missing from the table. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.3 & 0.4 & ? & 0.1 \end{array}$ $μ = 11$ , $σ \approx 9.43$ Let $X$ be the number of calls a help desk gets in a minute. It takes the values 0, 1, 2 and 3 with probabilities 0.1, 0.2, 0.4 and 0.3, in that order. Find the mean and the standard deviation of $X$ , to the nearest hundredth. $μ = 1.9$ , $σ \approx 0.94$ A spinner has 10 equal sections: 4 marked 1, 3 marked 2, 2 marked 3 and 1 marked 4. It is spun once, and $X$ is the number it lands on. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $μ = 2$ , $σ \approx 1.00$ Let $X$ be the points a team earns for one answer on a quiz show. One probability is missing from the table. Find $μ$ and $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.4 & 0.1 & ? & 0.1 \end{array}$ $μ = 12$ , $σ \approx 10.77$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Expected Value and Probability DistributionsAnswer keyVersion 2

Date Period

Answer each question.

Find the expected value from a table
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 16 & 10 & 6 & 3 \\ P (x) & \frac{5}{16} & \frac{3}{16} & \frac{1}{4} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{73}{8}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & - 4 & 15 & 5 \\ P (x) & \frac{7}{12} & \frac{1}{4} & \frac{1}{12} & \frac{1}{12} \end{array} \end{aligned}$ $\frac{19}{4}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 3 & 6 & 3 & 10 \\ P (x) & \frac{7}{12} & \frac{1}{12} & \frac{1}{12} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{3}{2}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & - 5 & 3 & - 2 & - 4 \\ P (x) & \frac{7}{16} & \frac{3}{8} & \frac{1}{16} & \frac{1}{8} \end{array} \end{aligned}$ $- \frac{27}{16}$
$\begin{aligned} Find the expected value. \\ \begin{array}{ccccc} x & 7 & 11 & 0 & - 5 \\ P (x) & \frac{7}{16} & \frac{3}{16} & \frac{1}{8} & \frac{1}{4} \end{array} \end{aligned}$ $\frac{31}{8}$

Find the expected profit or fair price
A ring toss costs $$ 4.00$ for one throw, which wins a prize of $$ 10.86$ with probability $\frac{1}{2}$ , or nothing; the $$ 4.00$ is not given back. Someone pays for $25$ throws. Find their expected total profit. $$ 35.75$
A game costs $$ 5.00$ to play. It pays out a prize of $$ 58.80$ with probability $\frac{1}{20}$ and a prize of $$ 9.00$ with probability $\frac{7}{20}$ , and otherwise nothing; the $$ 5.00$ is not returned. What should one play cost for the game to be fair? $$ 6.09$
A raffle ticket costs $$ 4.00$ . It wins a prize of $$ 16.62$ with probability $\frac{1}{6}$ , and nothing otherwise; the ticket price is not returned. Find the expected profit of one ticket for the player. $- $ 1.23$
A prize wheel at a fair costs $$ 4.00$ a spin. A spin wins a prize of $$ 9.18$ with probability $\frac{1}{6}$ , and otherwise nothing; the $$ 4.00$ is kept. What price for one spin would make the expected profit zero? $$ 1.53$
A scratch card sells for $$ 5.00$ . It pays out a prize of $$ 17.04$ with probability $\frac{1}{2}$ ; the $$ 5.00$ is not refunded. Someone pays for $10$ cards. Find their expected total profit. $$ 35.20$

Find the missing probability
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & ? & \frac{1}{8} & \frac{1}{4} & \frac{1}{8} \end{array} \end{aligned}$ $\frac{1}{2}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{2}{3} & \frac{1}{6} & ? & \frac{1}{12} \end{array} \end{aligned}$ $\frac{1}{12}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{5}{8} & \frac{1}{8} & \frac{1}{8} & ? \end{array} \end{aligned}$ $\frac{1}{8}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{2} & ? & \frac{1}{8} & \frac{1}{8} \end{array} \end{aligned}$ $\frac{1}{4}$
$\begin{aligned} Find the missing probability. \\ \begin{array}{ccccc} outcome & A & B & C & D \\ P & \frac{1}{6} & \frac{1}{3} & ? & \frac{1}{3} \end{array} \end{aligned}$ $\frac{1}{6}$

Find the mean and standard deviation
Let $X$ be the net points won in one round of a game (a negative value is a loss). Work out $μ$ and $σ$ for $X$ , to the nearest hundredth. $\begin{array}{ccccc} x & - 2 & - 1 & 0 & 1 \\ P (x) & 0.1 & 0.3 & 0.5 & 0.1 \end{array}$ $μ = - 0.4$ , $σ \approx 0.80$
Let $X$ be the prize, in dollars, won on a scratch card. One probability is missing from the table. What are the mean and the standard deviation of $X$ ? Round to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.3 & 0.4 & ? & 0.1 \end{array}$ $μ = 11$ , $σ \approx 9.43$
Let $X$ be the number of calls a help desk gets in a minute. It takes the values 0, 1, 2 and 3 with probabilities 0.1, 0.2, 0.4 and 0.3, in that order. Find the mean and the standard deviation of $X$ , to the nearest hundredth. $μ = 1.9$ , $σ \approx 0.94$
A spinner has 10 equal sections: 4 marked 1, 3 marked 2, 2 marked 3 and 1 marked 4. It is spun once, and $X$ is the number it lands on. Calculate the mean $μ$ of $X$ and its standard deviation $σ$ , to the nearest hundredth. $μ = 2$ , $σ \approx 1.00$
Let $X$ be the points a team earns for one answer on a quiz show. One probability is missing from the table. Find $μ$ and $σ$ , to the nearest hundredth. $\begin{array}{ccccc} x & 0 & 10 & 20 & 30 \\ P (x) & 0.4 & 0.1 & ? & 0.1 \end{array}$ $μ = 12$ , $σ \approx 10.77$

How to do these

Find the mean and the standard deviation, to the nearest hundredth. $\begin{array}{cccc} x & 1 & 2 & 3 \\ P (x) & 0.5 & 0.3 & 0.2 \end{array}$

Mean: 1(0.5) + 2(0.3) + 3(0.2) = 1.7.
Sum of x²P(x): 0.5 + 1.2 + 1.8 = 3.5.
Variance 3.5 - 1.7² = 0.61, and √0.61 ≈ 0.78.

The answer is $μ = 1.7$ , $σ \approx 0.78$ .

Where students go wrong

Leaving out the mean squared. The variance is the sum of x²P(x) minus μ², so stopping at 3.5 overstates it; here the variance is 0.61.

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.

Precalculus 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 Precalculus

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?+

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Are these expected value and probability distributions worksheets printable?+

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