Skill: probability-basics

Probability Practice

An endless supply of never-repeating probability problems with instant feedback. Compute theoretical probabilities for dice, coins, marbles, spinners, and cards — one at a time.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Probability

How to enter answers

Probabilities: a simplified fraction (1/2), a decimal (0.5), or a percent (50%). All three count as correct when the value matches.
Certain and impossible: 0 for impossible, 1 for certain.
Always simplify the fraction — 3/6 is marked “not simplest” where 1/2 is expected.

2 What you’ll practice

Every problem is generated fresh from 11 templates across three question types — a problem never repeats until its whole pool is used up.

Basic probability

Favorable over total: die rolls, marble bags, spinners, class picks, and card draws.

3 red of 8 sections → P = 3/8

Complements

P(not E) = 1 − P(E) — the fastest route when “not” appears.

P(not 6) = 1 − 1/6 = 5/6

Combined events

Tree diagrams for two coins, sums of two dice, and independent events with replacement — multiply for AND.

P(ace then king) = 1/13 × 1/13 = 1/169

3 Watch out for these

The three mistakes students make most often on probability problems.

1. Counting unequally likely outcomes

Wrong: “red or blue, so P(red) = 1/2.” Right: count individual equally likely outcomes — 1 red of 10 marbles is 1/10.

2. Adding instead of multiplying for AND

Wrong: P(ace then king) = 1/13 + 1/13. Right: multiply for independent AND: 1/169.

3. Skipping the simplification

Wrong: “P = 12/52” as the final answer. Right: 3/13 — reduce every probability.

Review the lesson Open the probability tool Print a worksheet