A fair six-sided die is rolled. What is the probability of an even number as a simplest fraction?
Answer and explanation
1/2
1/2
Subjects
Statistics & probability
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Sample exercises
A fair six-sided die is rolled. What is the probability of a result greater than 4?
Answer and explanation
1/3
1/3
A fair coin lands heads three times. The next independent toss has head probability
- 3/4
- 1/2
- 0
- 1
Answer and explanation
1/2
1/2
An event cannot happen in the defined sample space. Its probability is
- 0
- 1
- 2
- −1
Answer and explanation
0
0
An event is certain in the defined sample space. Its probability is
- 100 as a decimal probability
- 0
- 1
- −1
Answer and explanation
1
1
Why does counting red regions on a spinner not work if the regions have unequal angles?
Answer and explanation
Different regions may have different probabilities; their angular sizes, not just their count, matter in an ideal uniform spinner.
Different regions may have different probabilities; their angular sizes, not just their count, matter in an ideal uniform spinner.
Study notes
Combinations
Use combinations when order does not matter and items are chosen without replacement.
Grades 10–12Permutations
Use permutations when order matters and no item is repeated.
Grades 10–12Range of a data set
Sort the data or find its two extreme values.
Grades 4–8Weighted mean
Multiply each value by its frequency; divide by total frequency, not by the number of values.
Grades 9–12Complementary probability
An event and its complement cover all outcomes without overlap.
Grades 7–10Read and total a table
Add the counts for all categories.
Grades 1–3Two draws with replacement
Replacing the first item keeps the second probability unchanged.
Grades 7–10Conditional probability from counts
Restrict the denominator to the group named in the condition.
Grades 9–12Population variance
This is population variance: divide by N, not N − 1.
Grades 10–12Interquartile range
Use medians of the lower and upper halves for this exercise.
Grades 8–12Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 1–2Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 3–5Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 6–8Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 9–10Statistics & probability · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 11–12Probability: what a result does and does not show
Equal counting works only when the individual outcomes are equally likely.
Grades 6–10Probability: what a result does and does not show · revision card
Equal counting works only when the individual outcomes are equally likely.
Grades 6–10Data tables and fair summaries
Identify what is counted and make sure categories are not accidentally counted twice.
Grades 3–7Data tables and fair summaries · revision card
Identify what is counted and make sure categories are not accidentally counted twice.
Grades 3–7Data interpretation and misleading summaries
Check the axis, units, scale, population and sample size.
Grades 6–10Data interpretation and misleading summaries · Revision card
Check the axis, units, scale, population and sample size.
Grades 6–10Probability: choose the rule and check its conditions
Do not assume independence or mutual exclusion unless justified.
Grades 9–12Summaries, spread and missing context
Choose a numerical summary that matches the question and the data.
Grades 6–10Summaries, spread and missing context · Revision sheet
Choose a numerical summary that matches the question and the data.
Grades 6–10Descriptive statistics
The arithmetic average of numerical observations.
UniversityDescriptive statistics · revision notes
The arithmetic average of numerical observations.
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