Lesson Guide
Explanation
A probability is the number of ways something can happen over the total number of outcomes. In a bag with three red counters and five blue, there are eight counters altogether, so the chance of red is three out of eight and the chance of blue is five out of eight. Those two add to eight out of eight, which is one — a useful check. The commonest error is putting the other colour on the bottom instead of the total.
Your Turn
A bag has 2 green and 6 yellow counters. What is the chance of green? Check: 2 out of 8.
Watch Out
The bottom number is the TOTAL of everything, not the count of the other kind.
Explanation
Every probability lives on a line from nought to one. Nought means it cannot happen — rolling a seven on an ordinary die — and one means it must, like rolling a number less than seven. An even chance sits right in the middle at a half, and three out of eight is a little below the middle because four out of eight would be exactly a half. The line is also a check: any answer bigger than one, or a percentage over a hundred, is impossible.
Your Turn
Is 3 out of 8 likely or unlikely? Check: unlikely — it is less than a half.
Watch Out
A probability can never be more than 1. An answer of 5, or of 120%, means something went wrong.
Explanation
The same chance can be written three ways. To go from a fraction to a decimal, divide the top by the bottom; to go from a decimal to a percentage, multiply by a hundred. One divided by four is nought point two five, which is twenty-five per cent. It is worth learning the common ones by heart — a half is fifty per cent, a quarter twenty-five, three quarters seventy-five, a tenth ten and a fifth twenty — because almost every question uses one of them.
Your Turn
Write 1/5 as a decimal and a percentage. Check: 0.2 and 20%.
Watch Out
Divide top by bottom, in that order. 4 ÷ 1 = 4 is not a probability.
Explanation
Something either happens or it does not, so those two chances add to one. If the chance of landing on blue is a quarter, the chance of not landing on blue is one take a quarter, three quarters — seventy-five per cent. If the chance of rain is thirty per cent, the chance of no rain is seventy. Subtracting from one is usually much quicker than counting up all the other outcomes, especially when there are a lot of them.
Your Turn
The chance of rain is 30%. What is the chance of no rain? Check: 70%.
Watch Out
Subtract from 1 (or from 100%), not from the fraction's top number.
Explanation
Three moves cover the chapter: count the ways over the total, convert to whatever form the question asks for, and subtract from one when the question says not. Then check that the answer lands between nought and one, because an impossible number means a mistake somewhere earlier. Quiz and exercises now.
Your Turn
What is the chance of rolling a number less than 7 on an ordinary die? Check: 1 — it is certain.
Watch Out
Answer in the form asked for. "As a percentage" wants 25%, not 1/4.
📌 Key Points — this lesson in a nutshell
- A probability is the number of ways it can happen, over the total number of outcomes.
- Every probability sits between 0 (impossible) and 1 (certain). Nothing can be outside that.
- The same chance can be written as a fraction, a decimal or a percentage: ¼ = 0.25 = 25%.
- The chance of something not happening is 1 − the chance it does.
Step 1: Introduction
Step 1 of 5
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