Mathematics • Year 7 • Unit 4 • Lesson 15
The Probability Scale — Real World
Apply scale words, conversions and complement to real situations: a weather app, a spinner-based fete game, exam results, hospital surgery rates and a sports forecaster's odds.
1. Word problems
Each scenario asks you to convert, place on the scale, or apply the complement rule. Quote specific values.
1.1 — Weather app. A weather app shows: "70% chance of rain tomorrow."
(a) Convert 70% to a decimal and a fraction.
(b) Which scale word best describes this? (impossible / unlikely / even chance / likely / certain)
(c) What is P(no rain)? 3 marks
1.2 — Fete spinner. A 10-section spinner has 3 red, 4 blue and 3 green sections. The fete organiser tells you "You win if you spin BLUE."
(a) Calculate P(blue) as a fraction, decimal and percentage.
(b) Which scale word best describes P(blue)?
(c) Calculate P(not blue). 3 marks
1.3 — Hospital surgery. A surgeon tells a patient: "This operation has an 85% success rate."
(a) Convert 85% to a decimal.
(b) Which scale word fits?
(c) What is P(operation NOT successful)?
(d) In one sentence, explain whether you would describe this operation as "safe" — justify with the probability. 4 marks
1.4 — Sports odds. A sports forecaster says: "Team Falcons have a 3/5 chance of winning Saturday's match. The chance of a draw is 1/10."
(a) Convert 3/5 to a decimal and a percentage.
(b) Using the complement rule, calculate P(Team Bears win) (assume only three outcomes: Falcons win, Bears win, or draw).
(c) Order the three probabilities (Falcons win, Bears win, draw) from smallest to largest. 4 marks
1.5 — Exam pass. A teacher tells the class: "The probability of passing the exam this term is 0.85."
(a) Convert 0.85 to a percentage and a fraction.
(b) What is P(failing)?
(c) If 40 students sit the exam, about how many would you expect to pass? 3 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 Two friends are arguing about the probability of rain tomorrow. Sam says "It's 80% certain to rain." Alex replies "Wait — 80% isn't CERTAIN, it just means likely." Explain (i) which friend is correct, (ii) what "certain" means on the probability scale (P value), (iii) what "likely" means (P range), and (iv) why the everyday word "certain" can be misleading when used loosely.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Weather app
(a) 70% = 0.7 = 7/10.
(b) Scale word: likely (0.5 < 0.7 < 1).
(c) P(no rain) = 1 − 0.7 = 0.3 (30%).
1.2 — Fete spinner
(a) P(blue) = 4/10 = 2/5 = 0.4 = 40%.
(b) Scale word: unlikely (less than 0.5).
(c) P(not blue) = 1 − 0.4 = 0.6 (or 6/10 = 3/5).
1.3 — Hospital surgery
(a) 85% = 0.85.
(b) Scale word: likely (well above 0.5, but not quite certain).
(c) P(not successful) = 1 − 0.85 = 0.15 (15%).
(d) Sample: an 85% success rate is high, so most patients have a successful operation, but 15% (about 1 in 7) do not — so "safe" is reasonable for most patients, though not guaranteed.
1.4 — Sports odds
(a) 3/5 = 0.6 = 60%.
(b) P(Falcons) + P(draw) + P(Bears) = 1. So 0.6 + 0.1 + P(Bears) = 1 → P(Bears) = 0.3.
(c) Smallest to largest: draw (0.1) < Bears (0.3) < Falcons (0.6).
1.5 — Exam pass
(a) 0.85 = 85% = 17/20 (85/100 = 17/20).
(b) P(fail) = 1 − 0.85 = 0.15.
(c) Expected passes = 0.85 × 40 = 34 students.
2.1 — Explain your thinking (sample response)
(i) Alex is correct. (ii) On the probability scale, "certain" means P = exactly 1 (100%) — the event WILL happen. (iii) "Likely" means 0.5 < P < 1 — the event probably will happen, but there is still some chance it won't. (iv) The everyday word "certain" is misleading because in normal speech we sometimes say "80% certain" to mean "very likely". In mathematics, "certain" is reserved for P = 1 only. An 80% probability is "likely", not "certain" — there is still a 20% chance it does not happen.
Marking: 1 for naming Alex; 1 for P(certain) = 1; 1 for P(likely) = 0.5–1; 1 for the everyday vs maths distinction.