Mathematics • Year 7 • Unit 4 • Lesson 15
The Probability Scale — Mixed Challenge
Bring together the scale words, conversions between fractions / decimals / percentages, the complement rule, and ordering. Spot a confused student's mistake, then design events to land at specific positions on the scale.
1. Mixed problems
Each question uses scale words, conversions, ordering or complements. Show your working. 2 marks each
1.1 Convert P = 2/5 to a decimal and a percentage.
1.2 Place these four values in order from smallest to largest: 0.6, 1/3, 70%, 3/8.
1.3 P(event) = 9/10. (i) Convert to a decimal and a percentage. (ii) Which scale word best fits — likely or certain? Justify.
1.4 Match each event to a scale word: (i) Rolling a 10 on a standard die. (ii) Flipping heads on a coin. (iii) Drawing the ace of spades from a shuffled deck on the first try. (iv) The sun rising tomorrow.
1.5 A weather app gives P(rain) = 0.4. Use the complement rule to find P(no rain). Then convert both probabilities to percentages.
1.6 Of the events below, which is closest to "certain"? Convert all to decimals to compare. A: P = 3/5. B: P = 70%. C: P = 0.9. D: P = 4/6.
2. Find the mistake
A Year 7 student wrote the following solution. Exactly one line contains an error. 3 marks
Problem: Convert 0.4 to a percentage and a simplified fraction, then state P(complement) and the scale word for 0.4.
Line 1: Percentage: 0.4 × 100 = 40%.
Line 2: Fraction: 0.4 = 40/100 = 4/10 = 2/5.
Line 3: Complement: P(not event) = 1 − 0.4 = 0.6.
Line 4: Scale word for 0.4: "even chance" (since 0.4 is close to the middle).
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write the corrected statement.
Stuck? "Even chance" is reserved for P = 0.5 exactly, NOT "close to 0.5".3. Open-ended challenge — invent events for each scale word
This question has many correct answers. Show your work clearly. 4 marks
3.1 You are designing a probability poster for Year 7 with FIVE example events — one for each scale word. The events must:
- be real-world (not "rolling a 6 on a die" — too obvious),
- include the probability as a fraction, decimal AND percentage,
- match the correct scale word.
For each scale word: (i) write the event, (ii) state P as fraction = decimal = % , (iii) state the scale word, (iv) write ONE sentence on why it fits the word.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — 2/5
Decimal = 2 ÷ 5 = 0.4. Percentage = 0.4 × 100 = 40%.
1.2 — Ordering
Convert to decimals: 0.6, 1/3 ≈ 0.333, 70% = 0.7, 3/8 = 0.375.
Order smallest to largest: 1/3 (≈0.333) < 3/8 (0.375) < 0.6 < 70% (0.7).
1.3 — P = 9/10
(i) Decimal = 0.9. Percentage = 90%.
(ii) Scale word: likely (not certain — "certain" requires P = exactly 1, and 0.9 < 1).
1.4 — Match events to scale words
(i) Rolling a 10 on a standard die → impossible (P = 0).
(ii) Flipping heads on a coin → even chance (P = 0.5).
(iii) Drawing the ace of spades on first try → unlikely (P = 1/52 ≈ 0.019).
(iv) The sun rising tomorrow → certain (P = 1).
1.5 — Complement and percentages
P(no rain) = 1 − 0.4 = 0.6. P(rain) = 40%. P(no rain) = 60%.
1.6 — Closest to certain
Convert to decimals: A = 0.6, B = 0.7, C = 0.9, D = 4/6 ≈ 0.667.
Closest to 1 (certain): C = 0.9.
2 — Find the mistake
(a) The mistake is on Line 4.
(b) "Even chance" is reserved for P = exactly 0.5. P = 0.4 is LESS than 0.5, so it falls in the unlikely region, not "even chance".
(c) Corrected: Scale word for 0.4: "unlikely" (since 0.4 < 0.5).
3 — Probability poster (sample design)
Impossible: Snowing in Bondi Beach in January. P = 0/365 = 0 = 0%. Scale word: impossible. (Never observed in summer at sea level.)
Unlikely: A Year 7 student being the school captain (1 student out of about 180 in Year 7). P = 1/180 ≈ 0.006 ≈ 0.6%. Scale word: unlikely (close to 0).
Even chance: Guessing correctly on a true/false question. P = 1/2 = 0.5 = 50%. Scale word: even chance (exactly half).
Likely: A randomly picked Year 7 student owning a mobile phone (say 8 in 10). P = 8/10 = 0.8 = 80%. Scale word: likely (more than 50%).
Certain: A flipped coin landing as either heads or tails (no other outcome possible). P = 1 = 100%. Scale word: certain (one of the two MUST happen).
Marking: 1 mark per scale word for a valid real-world event with all three forms (fraction = decimal = %).