A7LAM CSCA ACADEMYCSCA Academy / Mathematics / Probability and statistics
CSCA Mathematics · Lesson 15 of 16Counting and probability
Dénombrement et probabilités · العدّ والاحتمالات
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Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Statistics summarises data with a few numbers.
Key ideas
- P(A) = favourable outcomes / total outcomes, when outcomes are equally likely.
- P(not A) = 1 − P(A).
- For independent events, P(A and B) = P(A) · P(B).
- Mean = sum ÷ count. Median = middle value of the sorted list.
Formulas to know
- Combinations: C(n, k) = n! / (k!(n − k)!)
- Permutations: P(n, k) = n! / (n − k)!
- P(A or B) = P(A) + P(B) − P(A and B)
Worked example
Two fair coins are tossed. What is the probability of getting two heads?
- The coins are independent.
- P(H) = 1/2 for each coin.
- P(H and H) = 1/2 × 1/2.
Answer: 1/4
Practice questions
1. Mean of 4, 8, 6, 10, 12?
6 · 8 ✓ · 9 · 10
Sum = 40, count = 5, mean = 8.
2. C(5, 2) = ?
10 ✓ · 20 · 25 · 5
5! / (2! · 3!) = 120 / 12 = 10.
3. A bag has 3 red and 5 blue balls. One is drawn at random. P(red) = ?
3/5 · 3/8 ✓ · 5/8 · 1/3
3 red out of 8 balls.