Place any event on a scale from 0 to 1 — and express it as a fraction, decimal, or percentage.
Print or save as PDF — or build a custom worksheet from any module's questions.
Doctors say a surgery has an 80% success rate. Weather forecasters say there's a 0.3 chance of rain. Bookmakers express odds as fractions like 3/4. All of these are the same probability — just written in different forms. Understanding the probability scale means you can interpret any of these at a glance and compare them confidently.
All probabilities sit on a scale from 0 to 1. The words we use — impossible, unlikely, even chance, likely, certain — match specific positions on this scale. Any probability can be written as a fraction, decimal, or percentage. These are just three ways to express the same number.
$$\frac{3}{4} = 0.75 = 75\%$$
The probability scale runs from 0 (impossible) to 1 (certain). Every event sits at exactly one point on this scale. Words like "likely" and "unlikely" describe regions, not exact values.
0: Impossible — rolling a 9 on a standard die.
0 to 0.5 (exclusive): Unlikely — drawing a spade from a shuffled deck (P = 1/4 = 0.25).
0.5: Even chance — flipping heads on a fair coin.
0.5 to 1 (exclusive): Likely — rolling a number less than 5 on a die (P = 4/6 ≈ 0.67).
1: Certain — rolling a number less than 10 on a standard die.
Probability can be expressed in three equivalent forms. You need to move fluently between them.
Fraction → Decimal: Divide top by bottom. $\frac{3}{4} = 3 \div 4 = 0.75$
Decimal → Percentage: Multiply by 100. $0.75 \times 100 = 75\%$
Percentage → Decimal: Divide by 100. $75\% \div 100 = 0.75$
Decimal → Fraction: Write over 10, 100, etc. $0.6 = \frac{6}{10} = \frac{3}{5}$
Always simplify fractions where possible. Check: does your final answer sit sensibly between 0 and 1?
To place an event on the probability scale: calculate its probability as a decimal, then locate that value between 0 and 1. Label the scale position clearly.
Rolling an odd number on a die: {1,3,5} → P = 3/6 = 0.5 → even chance (midpoint).
Drawing a heart from a deck: 13/52 = 1/4 = 0.25 → unlikely (1/4 of the way from 0).
Picking a consonant from {B,C,D}: 3/3 = 1 → certain (right end).
When comparing events, convert to the same form (all decimals is often easiest) before comparing positions.
Divide the numerator by the denominator.
$$\frac{3}{4} = 3 \div 4 = 0.75$$
Multiply the decimal by 100.
$$0.75 \times 100 = 75\%$$
P = 0.75 sits between 0.5 and 1 — it is in the likely region of the probability scale, three-quarters of the way from impossible to certain.
A: Rolling a 1 on a die → P = 1/6 ≈ 0.17
B: Flipping tails on a coin → P = 1/2 = 0.5
C: Drawing a red card from a deck → P = 26/52 = 0.5
D: Rolling less than 6 on a die → P = 5/6 ≈ 0.83
E: Rolling 7 on a standard die → P = 0
E (0) < A (≈0.17) < B = C (0.5) < D (≈0.83)
Note: B and C are at the same position — both have P = 0.5.
E → Impossible | A → Unlikely | B, C → Even chance | D → Likely
None of these events are certain (P = 1), so no event sits at the right endpoint.
Divide by 100 to convert percentage to decimal.
$$35\% \div 100 = 0.35$$
Write as a fraction over 100, then simplify.
$$0.35 = \frac{35}{100} = \frac{7}{20}$$
GCF of 35 and 100 is 5: 35 ÷ 5 = 7, 100 ÷ 5 = 20.
P = 0.35 < 0.5, so this event is in the unlikely region — it could happen, but probably won't.
Probability scale: 0 (impossible) → 0.5 (even chance) → 1 (certain).
Scale words: impossible (P=0), unlikely (0<P<0.5), even chance (P=0.5), likely (0.5<P<1), certain (P=1).
Converting: Fraction → Decimal (divide). Decimal → % (× 100). % → Decimal (÷ 100). Decimal → Fraction (write over 100, simplify).
Key rule: Probability is ALWAYS between 0 and 1 inclusive. Never write probability as a raw percentage number without the % symbol.
Convert 2/5 to a decimal and a percentage.
Decimal: 2 ÷ 5 = 0.4
Percentage: 0.4 × 100 = 40%
Convert P = 0.35 to a percentage and a simplified fraction.
Percentage: 0.35 × 100 = 35%
Fraction: 35/100 = 7/20 (divide by GCF 5)
Give one example of an event for each of these scale words: impossible, unlikely, even chance, likely, certain.
Impossible (P=0): Rolling a 10 on a standard die.
Unlikely (0 < P < 0.5): Rolling a 1 on a standard die (P = 1/6 ≈ 0.17).
Even chance (P=0.5): Flipping heads on a fair coin.
Likely (0.5 < P < 1): Rolling a number less than 5 on a die (P = 4/6 ≈ 0.67).
Certain (P=1): Rolling a whole number less than 10 on a standard die.
Is P(rolling ≤ 4 on a standard die) closer to 0 or 1? Explain and calculate.
Favourable outcomes: {1, 2, 3, 4} → 4 outcomes. Total: 6.
P = 4/6 = 2/3 ≈ 0.67
Since 0.67 > 0.5, it is closer to 1. This event is in the "likely" region of the scale.
1. On the probability scale, an event with an "even chance" is located at:
2. P(event) = 3/8. Which scale word best describes this event?
3. A weather forecast gives a 65% chance of rain. What is this as a decimal?
4. Which fraction is equivalent to the decimal 0.4?
5. Which event is closest to "certain" on the probability scale?
Q6. A spinner is divided into 10 equal sections: 3 red, 4 blue, 3 green.
(a) Calculate P(blue) as a fraction, decimal, and percentage.
(b) Where does P(blue) sit on the probability scale? Name the scale word.
(c) Calculate P(not blue).
Q7. Order the following probabilities from smallest to largest and label each with a scale word:
A = 7/10 B = 0.15 C = 50% D = 1/3 E = 0
Q8. A student writes: "The probability of passing the exam is 85%, so P(failing) = 15%."
(a) Rewrite both probabilities as decimals.
(b) Is the student's reasoning correct? Explain using the complement rule.
Q6.
(a) P(blue) = 4/10 = 2/5 = 0.4 = 40%
(b) P = 0.4 < 0.5 → this is in the unlikely region of the scale.
(c) P(not blue) = 1 − 0.4 = 0.6
Q7. 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
Q8.
(a) P(pass) = 85% ÷ 100 = 0.85; P(fail) = 15% ÷ 100 = 0.15
(b) Yes, the student is correct. Since "passing" and "failing" are complementary events (you either pass or fail — no other option), P(fail) = 1 − P(pass) = 1 − 0.85 = 0.15. The two probabilities sum to 1.
A sports journalist writes these three probability statements about tomorrow's match:
(a) Convert all three probabilities to decimals.
(b) Do all three probabilities sum to 1? If not, what is wrong?
(c) The journalist later says: "Actually, Team A winning or Team B winning are the only two possible outcomes — no draw is possible." Recalculate the probability of Team B winning using the complement rule.
(d) With only two possible outcomes (A wins or B wins), what must P(A wins) + P(B wins) equal? Use your answer from (c) to verify.
A probability of 0.5 means an even chance — equally likely to happen or not.
To convert a decimal to a percentage you divide by 100.
P = 0.7 is in the "likely" region of the probability scale.
Writing P = 50 is acceptable when the probability is 50%.