Probability and Statistics: Year 8 Study Guide
Data and chance help us make decisions when the answer is not certain.
Probability = number of favourable outcomes ÷ total outcomes, a number from 0 to 1. The complement of an event is 'not E': P(not E) = 1 − P(E). A sample space lists all possible outcomes. Two events are mutually exclusive if they cannot both happen; for these, P(A or B) = P(A) + P(B).
A Venn diagram shows how groups overlap. A two-way table sorts data by two categories. In statistics, mean, median, mode and range summarise data, and graphs such as histograms, box plots and scatter plots display it.
Venn diagrams and two-way tables
In a class of 30: 18 play netball, 14 play soccer, 6 play both. Only netball = 12, only soccer = 8, both = 6, neither = 30 − 26 = 4. P(plays at least one) = 26/30 = 13/15.
| Plays soccer | Does not play soccer | Total | |
|---|---|---|---|
| Plays netball | 6 | 12 | 18 |
| Does not play netball | 8 | 4 | 12 |
| Total | 14 | 16 | 30 |
Compound events
List outcomes for two coins: HH, HT, TH, TT. P(two heads) = 1/4. For rolling two dice, there are 36 outcomes; P(sum 7) = 6/36 = 1/6. Use a table or tree diagram. When events are independent (one does not affect the other), multiply: P(heads then a 6) = 1/2 × 1/6 = 1/12.
Table or tree.
Check each.
Favourable ÷ total.
Fraction, decimal or percent.
Summarising and comparing data
For test scores 4, 6, 7, 7, 9, 10: mode = 7, median = 7, mean = 43 ÷ 6 ≈ 7.2, range = 6. A box plot shows the minimum, quartiles, median and maximum. To compare two sets, compare the centre (mean or median) and the spread (range). A scatter plot shows the relationship between two variables: points rising together show a positive association, but association does not prove causation.
Worked examples and common mistakes
Example: A bag has 4 red, 3 blue and 5 green marbles. P(not green) = 7/12. Common mistakes: adding probabilities for events that overlap, forgetting that probabilities sum to 1 and ignoring outliers when comparing means. Draw a diagram first.
Check your understanding: model answers
1. Primes are 2, 3, 5, so 3/6 = 1/2. 2. Ordered: 3, 4, 6, 8, 9, so 6. 3. 0.65.
✨ Key Takeaways
- Probability = favourable ÷ total.
- P(not E) = 1 − P(E).
- Use Venn diagrams and two-way tables.
- Compare both centre and spread.
💬 Questions for Discussion & Reflection
- A die is rolled. Find P(a prime).
- Find the median of 3, 9, 4, 8, 6.
- If P(rain) = 0.35, find P(no rain).
Print graph paper for graphs →