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Probability Reasoning

Maths · Year 6 Selective
Year 6
Lesson Guide
Explanation
A spinner does not remember what it just did. If the first spin landed on blue, blue is still one in four next time — not less likely because it has come up, and not more likely because it is on a run. After three heads in a row a coin is still an even chance. This is the claim the paper offers most often, precisely because the true answer is the one that feels wrong.
Your Turn
A die has shown 6 twice. What is the chance of a 6 next? Check: still 1 out of 6.
Watch Out
"It is due" and "it is on a streak" are both wrong. Each go is independent.
Explanation
A bag behaves differently from a spinner, because taking a counter out and keeping it really does change what is left. Three red of eight becomes two red of seven: one fewer red and one fewer counter altogether, so both numbers move. If instead the counter is put back, nothing has changed at all and the chance is three out of eight again. One word in the question — kept or replaced — decides which it is.
Your Turn
A bag has 3 red of 8. One red is taken and put back. What is the chance of red now? Check: still 3 out of 8.
Watch Out
Both numbers change when a counter is kept. 3 of 8 becomes 2 of 7, never 2 of 8.
Explanation
When a question lists the chance of every outcome, they add to exactly one, and that is the equation it is hiding. If red and blue take four tenths between them, green and yellow share six tenths; and if green is twice yellow, that six tenths splits into three parts of two tenths, so yellow is nought point two and green nought point four. Twice as likely means three parts, not two. Finish by checking that all four add back to one.
Your Turn
Green and yellow share 0.6 and green is twice yellow. Find each. Check: yellow 0.2, green 0.4.
Watch Out
Split into three parts when one is twice the other, and give two of them to the bigger one.
Explanation
Two words that look alike test different things. Most likely compares the outcomes with each other, so blue covering half a spinner beats red and green at a quarter each. But likely compares one outcome with a half, and blue is exactly a half, so it is an even chance rather than likely. An outcome can be the most likely without being likely, and that distinction is what the claim questions are built on.
Your Turn
Blue covers half a spinner. Is blue likely? Check: no — it is an even chance.
Watch Out
Read which word the claim uses. "Most likely" and "likely" give different answers here.
Explanation
Put together, the exam shape is three claims about what happens next given what has already happened. On a four-colour spinner that has landed on blue, the second spin is still one in four, blue is not now less likely, and all four colours remain equally likely — tick, cross, tick. The false statement is always the one that sounds like common sense. And notice that with a bag where the counter was kept, the second claim could well be true, so read the setup before the claims. Quiz and exercises now.
Your Turn
Marks of ✓, ✗, ✓ — which option do you want? Check: "1 and 3".
Watch Out
Decide first whether the setup has a memory. A spinner never does; a bag with counters kept out does.
📌 Key Points — this lesson in a nutshell
  • A spinner, coin or die has no memory. The first spin changes nothing about the second.
  • Taking something out and keeping it does change the next chance; putting it back does not.
  • The chances of all the outcomes add to exactly 1 — that is usually the equation the question hides.
  • "Most likely" beats the other outcomes; "likely" beats a half. An outcome can be the first without being the second.
Step 1: Introduction
Step 1 of 5
It landed on blue. What about next time? spin 1: bluespin 2:still 1 out of 4 Nothing about the spinner changed between spins, so nothing about the chances changed. "Blue just came up, so blue is less likely now" is FALSE. So is "blue is on a run, so blue is more likely". After three heads in a row, the next coin toss is still an even chance. This is the claim the paper offers most often, because it is the one that feels wrong.
One red counter is taken before: 3 red of 8 kept out: 2 red of 7 If the counter is kept out, BOTH numbers change: one fewer red and one fewer altogether. 3 out of 8 becomes 2 out of 7 — not 2 out of 8. If it is put back, nothing has changed and the chance is 3 out of 8 again. A bag is not a spinner: one word — kept or replaced — decides the whole question.
Four colours, and one is twice another colourredbluegreenyellowchance0.20.2?? 0.2 + 0.2 = 0.41 − 0.40.6 to share3 parts of 0.2green 0.4 The chances of every outcome add to exactly 1. That is the equation hiding in the question. Red and blue take 0.4, so green and yellow share 0.6. Green is twice yellow, so the 0.6 splits into three parts of 0.2: yellow 0.2 and green 0.4. Check: 0.2 + 0.2 + 0.4 + 0.2 = 1 ✓. "Twice as likely" splits the share into THREE parts, not two.
Two different tests blue ½ · red ¼ · green ¼ "Blue is most likely" → TRUE, it beats both "Blue is likely" → FALSE, it is exactly ½ most likely = biggest · likely = over a half "Most likely" compares the outcomes with each other; "likely" compares one with a half. An outcome can be the most likely and still not be likely — blue here is exactly an even chance. Even chance is exactly a half; likely is more than a half; unlikely is less.
The exam shape 1 · The second spin is still 1 in 4 for blue✓ 2 · Blue is now less likely than the others✗ 3 · All four colours are equally likely✓ Marked separately: ✓, ✗, ✓ — so the answer is "1 and 3". The false one is the one that sounds like common sense. That is exactly why it is there. If the question had said the counter was KEPT from a bag, statement 2 might well be true — read the setup. Spinner or bag · replaced or kept · most likely or likely. Quiz and exercises now.
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