Two events EEE and FFF have probabilities P(E)=pP(E) = pP(E)=p and P(F)=qP(F) = qP(F)=q. Express P(E∪F)P(E \cup F)P(E∪F) in terms of ppp and qqq when: (i) EEE and FFF are mutually exclusive, (ii) EEE and FFF are independent.
In a soil quality assessment, let AAA be the event that a sample contains Lead and BBB be the event that it contains Mercury. It is known that
P(A∩B′)=0.45,P(B)=0.35andP(A∣B)=0.6 P(A \cap B') = 0.45, \quad P(B) = 0.35 \quad \text{and} \quad P(A|B) = 0.6 P(A∩B′)=0.45,P(B)=0.35andP(A∣B)=0.6Find the value of: P(A∪B)P(A \cup B)P(A∪B)
P(A∩B)P(A \cap B)P(A∩B)
P(A)P(A)P(A)
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.