Probability distributions Worksheets
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Easy
10 problemsMedium
20 problemsHard
20 problemsMixed
30 problemsFree printable probability distributions worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from expected value e(x) of a discrete variable at the easy level through to normal distribution: p(x < a), p(x > a), p(a < x < b) at the advanced level.
What is probability distributions?
A probability distribution describes how likely different outcomes are in a random event or experiment. It shows the full picture of what could happen and assigns a probability to each possible result, whether you're rolling dice, measuring heights, or counting defects in a factory.
Understanding distributions is essential for interpreting data in science, economics, and everyday decision-making. Students will use these concepts in advanced statistics, calculus, and any field that deals with uncertainty, from polling and quality control to weather forecasting and medical research.
Pick a difficulty
Click any level to open the generator with that difficulty pre-selected.
Beginner
Generate →- Concepts
- Expected value E(X) of a discrete variable
- Range
- 3–4 values, probabilities in tenths
- Steps
- 2 steps
- Example
- E(X) = Σ xᵢ·P(xᵢ)
Easy
Generate →- Concepts
- Find a missing probability, then E(X)
- Range
- 3–4 values, probabilities in tenths
- Steps
- 2–3 steps
- Example
- Σ P(xᵢ) = 1 → find the missing P
Medium
Generate →- Concepts
- Variance Var(X) and standard deviation SD(X)
- Range
- 3–4 values, probabilities in tenths
- Steps
- 3 steps
- Example
- Var(X) = Σ xᵢ²·P(xᵢ) − E(X)²
Hard
Generate →- Concepts
- Normal distribution: P(X < a), P(X > a), P(a < X < b)
- Range
- μ, σ integers; z to 2 decimals
- Steps
- 2–3 steps
- Example
- z = (a − μ)/σ, P(X < a) = Φ(z)
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