Unit 2 – Probability · Both
Probability – Conditional & Venn Diagrams
Venn diagrams, mutually exclusive and independent events, and conditional probability.
Beyond basic probability you need Venn diagrams, the language of exclusive and independent events, and conditional probability (especially Higher).
Mutually exclusive and independent
**Mutually exclusive** – cannot happen at the same time.
P(A or B) = P(A) + P(B)
**Independent** – one does not affect the other.
P(A and B) = P(A) × P(B)
Venn diagrams
Show sets and overlaps.
• Intersection A ∩ B – in both
• Union A ∪ B – in A or B or both
• Complement – not in the set
Frequencies or probabilities can be written in each region.
Conditional probability
P(A given B) = P(A and B) / P(B)
Written P(A|B).
“Given that” means restrict to the relevant group first.
Worked example
P(A) = 0.6, P(A and B) = 0.2. Find P(B|A).
Solution
P(B|A) = 0.2 / 0.6 = **1/3**
Practice questions
Try these without looking at the answers first.
Q1.If events are independent, P(A and B) = ?
Show answer
P(A) × P(B)
Q2.P(A and B) = 0.15, P(B) = 0.5. P(A|B)?
Show answer
0.3