sample spaces, combined events and complements
List every outcome of a coin and a spinner, two coins and two dice. Find the favourable cells in a 6 × 6 grid, and get the probability that something doesn't happen from the probability that it does.
- UK: Year 8
- France: grade 5
- Germany: grade 8
- Iran: grade 8
- Afghanistan: grade 7
- Syria: grade 7
- Palestine: grade 4
- Ukraine: grade 9
- Russia: grade 7
Guide
This studio follows Iran's Year 8 lesson «بررسی حالتهای ممکن», Year 9 «مجموعهها و احتمال» and the KS3 work on sample spaces for single and combined events. The sample space is the set of all possible outcomes. When two things are used together (a coin and a spinner, two dice), each outcome is a pair, and the number of outcomes multiplies: 2 × 3 = 6 and 6 × 6 = 36.
In the two-dice grid the first dice runs down the side and the second across the top. Each cell is one outcome. Tap the cells of an event to count them.
Common mistakes: "the totals 2 to 12 are equally likely" (there are 11 totals but 36 equally likely outcomes); counting (H, T) and (T, H) as one outcome; writing P(A′) = 1 + P(A) or 1 ÷ P(A) instead of P(A′) = 1 − P(A); listing an outcome twice.