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Probability as a Decimal: Parts That Sum to 1

Maths · Stage 3
Year 5
Lesson Guide
Explanation
A probability is a number that says how likely something is, from zero for impossible to one for certain. A coin landing heads is a half, or zero point five. A six on a die is a sixth. The sun rising is one; a seven on an ordinary die is zero. You can write a probability as a fraction or a decimal, and the tests use both. Anything above one, or below zero, cannot be a probability. Likely means more than zero point five; unlikely means less.
Your Turn
Write as decimals: 1/2, 3/4, 1/10. Check: 0.5, 0.75, 0.1.
Watch Out
Probability is never bigger than 1. If your answer is 1.2, something was counted twice.
Explanation
When every outcome is equally likely, the probability of what you want is the number of ways it can happen divided by the total number of outcomes. A spinner with four equal sectors, one red: one quarter, zero point two five. Five equal sectors, two red: two fifths, zero point four. Ten counters, three red: three tenths, zero point three. Count the total, count the favourable ones, divide, and write it as a decimal if the question wants one.
Your Turn
A bag has 20 counters, 5 of them red. P(red) as a decimal? Check: 5/20 = 1/4 = 0.25.
Watch Out
The sectors must be EQUAL for counting to work. A spinner that is half red and quarter blue is not "two colours, so 1/2 each".
Explanation
Something has to happen, so the probabilities of all the possible outcomes add to one. If red is zero point five and blue is zero point three, green must be one minus zero point eight, zero point two. The same idea gives the probability of not something: not red is one minus red. Whenever a question hands you probabilities, add them as a check — they cannot come to more than one. And add decimals with the points lined up, as in the decimals lesson.
Your Turn
P(A) = 0.35. What is P(not A)? Check: 1 − 0.35 = 0.65.
Watch Out
1 − 0.35 is 0.65, not 0.75. Pad to 1.00 and subtract with the points lined up.
Explanation
Twice as likely means twice the probability. If blue is zero point two, a colour twice as likely as blue is zero point four. Half as likely would be zero point one; three times, zero point six. In counters it is the same picture: four blue out of twenty is zero point two, and twice as many red — eight — is zero point four. Doubling a decimal is ordinary doubling with the point kept in place: zero point one five doubles to zero point three.
Your Turn
Blue is 0.15 and red is twice as likely. P(red)? P(blue or red)? Check: 0.3; 0.45.
Watch Out
"Twice as likely as blue" multiplies BLUE's probability. It is not twice as likely as everything else.
Explanation
Now the selective paper's question. A bag of buttons: blue is zero point two, red is twice as likely as blue, green is zero point three, and the rest are yellow. First, red: twice zero point two, zero point four. Then the three known ones together: zero point two plus zero point four plus zero point three is zero point nine. Then yellow is one minus zero point nine, zero point one. Three ideas in one question, each easy, and the skill is doing them in order. Check that all four add to one. Quiz and exercises now.
Your Turn
P(A) = 0.25, P(B) is twice P(A), P(C) = 0.15. P(D)? Check: B = 0.5; total 0.9; D = 0.1.
Watch Out
Work out the "twice as likely" one BEFORE adding. The sum of the known probabilities has to include it.
📌 Key Points — this lesson in a nutshell
  • Probability is a number from 0 (impossible) to 1 (certain). A fraction or a decimal — 1/4 or 0.25.
  • Equally likely outcomes: probability = favourable ÷ total. 1 red sector of 4: 1/4 = 0.25.
  • The probabilities of all the outcomes add up to 1. So the last one is 1 minus the rest.
  • "Twice as likely" means double the probability: if blue is 0.2, red is 0.4.
Step 1: Introduction
Step 1 of 5
Impossible is 0, certain is 1, and everything else is in between 01impossible1/4even3/4certain A probability is a fraction of the way from impossible to certain. A coin landing heads: 1/2 = 0.5. A 6 on a die: 1/6. The sun rising tomorrow: 1. Rolling a 7 on a die: 0. Fractions and decimals are both fine: 1/4 = 0.25, 3/4 = 0.75, 1/10 = 0.1, 3/10 = 0.3. A number bigger than 1, like 1.2, cannot be a probability. Neither can a negative number. "Likely" is more than 0.5; "unlikely" is less. "Even chance" is exactly 0.5.
P(red) on a spinner with 4 equal sectors 1 of 4 red: 1/4 = 0.25 2 of 5 red: 2/5 = 0.4 When every outcome is equally likely: probability = favourable outcomes ÷ total outcomes. 10 counters, 3 red: P(red) = 3/10 = 0.3. 20 counters, 5 red: 5/20 = 1/4 = 0.25. 8 sectors, 3 shaded: 3/8 = 0.375. Count the total first. Then the ones you want. Then divide — and convert to a decimal if asked.
P(red) = 0.5, P(blue) = 0.3, P(green) = ? 01red 0.5+ blue 0.31 One of the colours must come up, so the probabilities of all of them add to 1. 0.5 + 0.3 = 0.8, so P(green) = 1 − 0.8 = 0.2. "Not red" is everything else: P(not red) = 1 − 0.5 = 0.5. P(A) = 0.35 → P(not A) = 0.65. Check the total whenever probabilities are given: if they add to more than 1, one of them is wrong. Line the decimals up at the point when adding: 0.5 + 0.3 + 0.2 = 1.0.
Blue is 0.2. Red is twice as likely as blue. 01blue 0.2blue + red = 0.6 Twice as likely means twice the probability: P(red) = 2 × 0.2 = 0.4. Blue and red together: 0.2 + 0.4 = 0.6. Half as likely as blue would be 0.1. Three times: 0.6. In counters: if there are 4 blue out of 20 (0.2), there are 8 red (0.4). "Twice as likely" is about the probability, not about adding 2. 0.2 + 2 makes no sense as a probability. Doubling a decimal: 0.2 → 0.4, 0.15 → 0.3, 0.35 → 0.7. Line up, double, keep the point.
Blue 0.2. Red twice as likely as blue. Green 0.3. What is yellow? 01blue 0.2+ red 0.4+ green 0.31 Step 1: red = 2 × 0.2 = 0.4. Step 2: blue + red + green = 0.2 + 0.4 + 0.3 = 0.9. Step 3: yellow = 1 − 0.9 = 0.1. Three ideas in one question: "twice as likely", adding decimals, and the total being 1. Each step is easy; the order is the skill. Trap: forgetting to double red, and getting 1 − 0.7 = 0.3. Trap: reading "twice as likely" as red = 0.2 + 2. Check: 0.2 + 0.4 + 0.3 + 0.1 = 1.0 ✓ Quiz and exercises now.
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