Probability

Single events, combined events, tree diagrams and Venn diagrams — with the with-and-without-replacement distinction that most of these questions turn on.

หลักสูตรแกนกลาง / สสวท.: สถิติและความน่าจะเป็น (Statistics and Probability)ครอบคลุม ม.3 บทที่ 9 และ ม.4 ความน่าจะเป็น
Common Core (US): S-CP, 7.SP
Cambridge: IGCSE 0580 — Topic 8: Probability (Core and Extended)

11.1 Single events

The basics

P (E) = \frac{n ( E )}{n ( S )} P (not E) = 1 - P (E) 0 \leq P (E) \leq 1

The counting formula assumes every outcome is equally likely — a fair die, a fair coin, a well-shuffled pack.

เคล็ดลับ

Whenever a question says "at least one", reach for the complement first. Counting "at least one" directly means several cases; counting "none" is usually a single calculation.

ตัวอย่าง

A spinner has $8$ equal sectors numbered $1$ to $8$ . Find the probability of scoring a prime number.

วิธีทำ

1.Primes from $1$ to $8$ : $2, 3, 5, 7$
2. $\frac{4}{8}$

ตอบ $\frac{1}{2}$

📖 2 more sections of this chapter are being checked

The whole chapter is written; we read it back section by section before releasing it, because maths nobody has checked should not be on a public page. What is open is complete — nothing here is abridged.

Read it — now practise it

Generate a worksheet on this topic, or sit a timed mock paper.

Build a worksheet Practice arena