IGCSE MATH: PROBABILITY

📘 IGCSE Mathematics - Probability Notes

Cambridge IGCSE Syllabus Reference

1. Calculate Probability of a Single Event

Definition: Probability measures how likely an event is to occur. It is expressed as a number between 0 and 1.

P(event) = Number of favorable outcomes ÷ Total possible outcomes

✨ Key Points:

Probability of 0 → Event is impossible
Probability of 1 → Event is certain
All probabilities are between 0 and 1 (inclusive)

📝 Example 1:

What is the probability of rolling a 4 on a fair six-sided die?

Favorable outcomes: 1 (only the number 4)

Total possible outcomes: 6

P(rolling a 4) = 1/6

2. The Probability Scale

0
Impossible

0.5
Even Chance

1
Certain

Impossible
P = 0

Unlikely
0 < P < 0.5

Even Chance
P = 0.5

Likely
0.5 < P < 1

Certain
P = 1

3. Complementary Events

P(A) + P(A') = 1

Where A' means "not A"

🎯 Useful Formulas:

P(A) = 1 − P(A')

P(A') = 1 − P(A)

4. Combined Events

AND Rule (Independent Events)

                    P(A AND B) = P(A) × P(B)
                

Example: Rolling two sixes: 1/6 × 1/6 = 1/36

OR Rule (Mutually Exclusive)

                    P(A OR B) = P(A) + P(B)
                

Example: Rolling a 3 or 5: 1/6 + 1/6 = 1/3

OR Rule (Non-Mutually Exclusive)

                    P(A OR B) = P(A) + P(B) − P(A AND B)
                

Example: Drawing a King or Heart from cards

5. Quick Reference - All Formulas

Basic Probability
P(A) = Favourable ÷ Total

Complement Rule
P(A') = 1 − P(A)

Relative Frequency
RF = Occurrences ÷ Trials

Expected Frequency
EF = Probability × Trials

🎯 Exam Success Tips

✓ Show Your Work

Always write down each step - marks are given for method!

✓ Fractions First

Use fractions unless asked for decimals/percentages

✓ Check Your Range

Probability must be between 0 and 1!

✓ Tree Diagrams

Label ALL branches with probabilities

🧠 Practice Questions

Question 1

A spinner has 8 sections: 3 red, 2 blue, 2 green, 1 yellow.

a) Find P(red)
b) Find P(not yellow)
c) Expected green in 200 spins?

Question 2

Two dice are rolled. Find:

a) P(both show 6)
b) P(sum is 7)
c) P(at least one shows 6)

Question 3

Bag: 4 red, 5 blue, 3 green marbles. Two drawn without replacement.

a) Draw tree diagram
b) Find P(both red)
c) Find P(one red, one blue)

🚀 Ready to Ace Your Exam!

Remember: Practice makes perfect! Good luck! 🎓