Mathematics • Year 8 • Unit 4 • Lesson 15
The Probability Scale
Build fluency with placing events on the 0-to-1 scale, converting between fractions/decimals/percentages, and comparing likelihoods. One worked example, one guided fill-in, then eight independent problems from quick labels to ordering five events.
1. I do — fully worked example
Read every line. Each step has a short reason.
Problem. Calculate the probability of drawing a King from a standard deck. Then label it impossible / unlikely / even chance / likely / certain, and write it as a fraction, decimal, and percentage.
Step 1 — Calculate the probability.
Favourable = 4 Kings Total = 52 cards P(King) = 4 ÷ 52 = 1/13
Reason: standard probability formula. Simplify the fraction (gcd 4 = 4).
Step 2 — Convert to decimal and percentage.
1/13 ≈ 0.077 0.077 × 100 ≈ 7.7%
Reason: divide top by bottom for decimal; × 100 for percentage.
Step 3 — Place on the probability scale.
0.077 is between 0 and 0.5, so the event is unlikely.
Reason: any value strictly between 0 and 0.5 is "unlikely" — it might happen, but won't most of the time.
Answer: P(King) = 1/13 ≈ 0.077 = 7.7%, labelled unlikely on the probability scale.
2. We do — fill in the missing steps
Same shape as Section 1, but the working is faded. Fill in each blank. 4 marks
Problem. A standard die is rolled. Find P(rolling a number greater than 2). Label it on the probability scale and write it as a fraction, decimal, and percentage.
Step 1 — Calculate the probability:
Favourable = {______, ______, ______, ______}, count = ______. Total = ______.
P(greater than 2) = ______ ÷ ______ = ______ (simplified)
Step 2 — Convert to decimal and percentage:
As a decimal ≈ ______. As a percentage ≈ ______%.
Step 3 — Place on the scale:
______ is between 0.5 and 1, so the event is ____________.
3. You do — independent practice
Show your working in the space under each problem. Foundation → Standard → Extension.
Foundation — quick labels
3.1 Label each event as impossible, unlikely, even chance, likely, or certain:
(a) Rolling a 7 on a standard die.
(b) Flipping heads on a fair coin.
(c) The sun rising tomorrow. 1 mark
3.2 Convert each probability to a percentage:
(a) 1/2 (b) 0.3 (c) 3/4 1 mark
3.3 Convert each percentage to a decimal:
(a) 20% (b) 65% (c) 100% 1 mark
3.4 Explain in one sentence the difference between "unlikely" and "impossible". 1 mark
Standard — calculate, convert, label
3.5 A spinner has 10 equal sectors: 1 sector is "WIN", 9 are "LOSE". Find P(WIN) as a fraction, decimal, and percentage. Label it on the scale. 2 marks
3.6 The probability of a footy team winning is 4/5. Convert this to a decimal and percentage. Label it on the scale. 2 marks
Extension — order events by likelihood
3.7 Calculate each probability and order from least to most likely:
Event A: rolling a 1 on a standard die.
Event B: flipping heads on a fair coin.
Event C: drawing an Ace from a standard deck.
Event D: rolling a number greater than 1 on a standard die.
Event E: rolling a 7 on a standard die. 3 marks
3.8 Compare 3/7 and 5/12 — which is greater? Convert both to decimals (3 d.p.) and explain how the decimal form makes comparison easier. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (greater than 2 on a die)
Step 1: Favourable = {3, 4, 5, 6}, count = 4. Total = 6. P = 4 ÷ 6 = 2/3.
Step 2: 2/3 ≈ 0.667 = 66.7%.
Step 3: 0.667 is between 0.5 and 1, so the event is likely.
3.1 — Quick labels
(a) Rolling a 7: impossible (P = 0). (b) Flipping heads: even chance (P = 0.5). (c) Sun rising: certain (P = 1).
3.2 — Fraction/decimal → %
(a) 1/2 = 50%. (b) 0.3 = 30%. (c) 3/4 = 75%.
3.3 — % → decimal
(a) 20% = 0.2. (b) 65% = 0.65. (c) 100% = 1.
3.4 — Unlikely vs impossible
Impossible means probability 0 — the event can never happen. Unlikely means probability between 0 and 0.5 — the event probably won't happen, but it still might.
3.5 — Spinner WIN
P(WIN) = 1/10 = 0.1 = 10%. Label: unlikely (between 0 and 0.5).
3.6 — Footy team
P(win) = 4/5 = 0.8 = 80%. Label: likely (between 0.5 and 1).
3.7 — Order by likelihood
Calculations: A = 1/6 ≈ 0.167; B = 1/2 = 0.5; C = 4/52 = 1/13 ≈ 0.077; D = 5/6 ≈ 0.833; E = 0/6 = 0.
Order (least to most likely): E (0) < C (0.077) < A (0.167) < B (0.5) < D (0.833).
3.8 — Compare 3/7 vs 5/12
3/7 ≈ 0.429. 5/12 ≈ 0.417. So 3/7 is greater. Decimals make comparison easy because you read left-to-right; with raw fractions and different denominators, you need to find a common denominator first or convert mentally — slower and more error-prone.