Given that P(A)=aP(A) = aP(A)=a and P(B)=bP(B) = bP(B)=b, state an expression for P(A∪B)P(A \cup B)P(A∪B) in terms of aaa and bbb when: (i) AAA and BBB are mutually exclusive, (ii) AAA and BBB are independent.
In a climate study, let HHH be the event of high humidity and TTT be the event of high temperature. It is found that:
P(H∩T′)=0.22,P(T)=0.30andP(H∣T)=0.6 P(H \cap T') = 0.22, \quad P(T) = 0.30 \quad \text{and} \quad P(H|T) = 0.6 P(H∩T′)=0.22,P(T)=0.30andP(H∣T)=0.6Find the value of: P(H∪T)P(H \cup T)P(H∪T)
P(H∩T)P(H \cap T)P(H∩T)
P(H)P(H)P(H)
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.