Reason with probability
Count the possible outcomes and choose the exact answer.
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Example
Example
- Exact probability
- 6 / 36 ≈ 16.7%
- Rolls
- 0
- Matches
- 0
- Observed frequency
- —
Each of the 36 pairs is equally likely. Sums with more pairs are more likely.
Coins, dice sums and at least one
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8 questions · No time limit
- Questions answered
- 0 / 8
- Active time
- 0:00
What can happen?
Read what is random and what is being counted. Choose the exact probability or expected point value.
One way to solve it
Explore the method
Keep outcomes equally likely before dividing favorable cases by all cases.
On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is usedHelp
Choose one of five answers. The answer locks when selected. Read the method, then choose Next question.
Count equally likely outcomes, not just different-looking results. Two dice have 36 ordered outcomes, but their sums are not equally likely.
All answers are exact. Fractions may represent probabilities or point values. For draws without replacement, the bag changes after the first draw.
Expected payout is the average points received over many repetitions, not a promised result on one roll. Expected net gain subtracts the fixed cost and can be negative.
Finish all eight questions to save a result in this browser. An unfinished round is not saved. Active time includes answers and review, but not background tabs. There is no time limit or speed bonus.
Use Tab and Enter or Space to choose an answer. Keys 1–5 also select answers, except when another control is focused.
About this practice
Learn a method
Count equally likely outcomesCount the possible outcomes and choose the exact answer.
For a broader mix of practices, explore the probability practice test. Sign in free to start a test.
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On by default unless you turn it off. Saved choices are kept. Shares starts, completions, replays and error categories. For ChatGPT visits, starts and completions may include the first QuickenBrain page and country. No answers, drawings or names.
How this data is used