Topic 5 of 7 · Form 3
Probability
P(A) = favourable outcomes ÷ total equally likely outcomes; complementary events; relative frequency and expected frequency.
Notes for this topic 1 file, in order
Create a free account to download PDFs.
Basic probability
P(A) = favourable outcomes ÷ total equally likely outcomes; complementary events; relative frequency and expected frequency.
Combined events
Sample spaces, Venn diagrams, tree diagrams; mutually exclusive events (P(A or B) = P(A) + P(B)); independent events (P(A and B) = P(A) × P(B)); general addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B); conditional probability P(A|B) = P(A ∩ B) ÷ P(B).
Worked example: P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3. Find P(A ∪ B) and P(A | B). Are A and B independent?
P(A ∪ B) = 0.6 + 0.5 − 0.3 = 0.8; P(A | B) = 0.3 ÷ 0.5 = 0.6 = P(A) → independent
Selection without replacement
Worked example: Two cards are drawn without replacement from 4 red and 6 black cards. Find P(both black).
6/10 × 5/9 = 1/3
Expectation
Expected value = Σ(value × probability); used to decide whether a game is fair.
Worked example: A game costs US$1. You win US$5 with probability 0.1 and nothing otherwise. Find the expected gain.
Expected winnings = 5 × 0.1 = 0.50 → expected gain = 0.50 − 1 = −US$0.50
Check yourself
- A die is rolled 300 times. Estimate the number of fives.
- P(rain) = 0.2 each day independently. Find P(no rain on two days).
- What makes a game fair?
Show answers
- 50
- 0.8 × 0.8 = 0.64
- The expected gain is zero.
Questions about this topic (0)
No questions about this topic yet.
Sign in or create a free account to join in.