Mathematics • Year 7 • Unit 4 • Lesson 15

The Probability Scale

Build fluency with the scale from 0 (impossible) to 1 (certain), the five scale words (impossible / unlikely / even chance / likely / certain), and converting between fractions, decimals and percentages.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step shows the question to ask and the reason for the answer.

Problem. Convert P = 3/4 to a decimal and a percentage, then place it on the probability scale and name its scale word.

Step 1 — Fraction → Decimal (divide top by bottom).

3/4 = 3 ÷ 4 = 0.75.

Reason: to convert a fraction to a decimal, divide the numerator by the denominator.

Step 2 — Decimal → Percentage (multiply by 100).

0.75 × 100 = 75%.

Reason: a percentage is "out of 100".

Step 3 — Place on the scale.

P = 0.75 lies between 0.5 and 1 — in the LIKELY region.

Reason: the scale word for 0.5 < P < 1 is "likely".

Answer: 3/4 = 0.75 = 75%. Scale word: LIKELY (three-quarters of the way from impossible to certain).

Stuck? Revisit lesson § "Converting Between Forms" — fraction ÷ for decimal, × 100 for percentage.

2. We do — fill in the missing conversions and scale words

Complete the conversion table and the scale-word column. 5 marks

Row 1: Fraction = 1/4. Decimal = ___ . Percentage = ___ % . Scale word = ___________ .

Row 2: Fraction = ___ . Decimal = 0.5. Percentage = ___ % . Scale word = ___________ .

Row 3: Fraction = ___ . Decimal = ___ . Percentage = 80% . Scale word = ___________ .

Row 4: Fraction = 0/6 = 0. Decimal = ___ . Percentage = ___ % . Scale word = ___________ .

Row 5: Fraction = 6/6 = 1. Decimal = ___ . Percentage = ___ % . Scale word = ___________ .

Stuck? P = 0 → impossible; 0 < P < 0.5 → unlikely; 0.5 → even chance; 0.5 < P < 1 → likely; P = 1 → certain.

3. You do — independent practice

Convert as asked. State scale words. Always check the answer is between 0 and 1.

Foundation — convert one form to another

3.1 Convert 1/2 to a decimal and a percentage. 1 mark

3.2 Convert 0.2 to a percentage and a simplified fraction. 1 mark

3.3 Convert 60% to a decimal and a simplified fraction. 1 mark

3.4 P = 1. What is the scale word and what does it mean? 1 mark

Standard — assign scale words

3.5 Convert P = 3/8 to a decimal. Then name the scale word. 2 marks

3.6 Order from smallest to largest, then assign a scale word to each: A = 7/10, B = 0.15, C = 50%, D = 1/3, E = 0. 3 marks

Extension — complement and same-form comparisons

3.7 Convert 35% to a decimal and a simplified fraction. Then state P(complement). 2 marks

3.8 A student writes "P = 50 because the chance is 50%." Explain in two sentences why this is wrong, and write the correct value. 2 marks

Stuck on 3.7? P(complement) = 1 − P(event).

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Answers — Do not peek before attempting

Section 2 — Conversion table (We do)

Row 1: 1/4 = 0.25 = 25%. Scale word: unlikely.
Row 2: 1/2 = 0.5 = 50%. Scale word: even chance.
Row 3: 4/5 = 0.8 = 80%. Scale word: likely.
Row 4: 0 = 0 = 0%. Scale word: impossible.
Row 5: 1 = 1 = 100%. Scale word: certain.

3.1 — 1/2

Decimal = 0.5. Percentage = 50%.

3.2 — 0.2

Percentage = 0.2 × 100 = 20%. Fraction = 2/10 = 1/5.

3.3 — 60%

Decimal = 60 ÷ 100 = 0.6. Fraction = 60/100 = 3/5.

3.4 — P = 1

Scale word: certain. It means the event will definitely happen.

3.5 — P = 3/8

Decimal = 3 ÷ 8 = 0.375. Scale word: unlikely (between 0 and 0.5).

3.6 — Order and scale words

Convert all to decimals: A = 0.7, B = 0.15, C = 0.5, D ≈ 0.333, E = 0.
Order: E (0) < B (0.15) < D (0.333) < C (0.5) < A (0.7).
Scale words: E = impossible, B = unlikely, D = unlikely, C = even chance, A = likely.

3.7 — 35%

Decimal = 0.35. Fraction = 35/100 = 7/20. Complement P(not event) = 1 − 0.35 = 0.65.

3.8 — P = 50 is wrong

P = 50 is wrong because probability is always between 0 and 1 — "P = 50" would mean 5000%, which is impossible. The correct value is P = 0.5 (or equivalently 50% or 1/2).