In a reliability study of a satellite system, the events A A\,A and B B\,B represent the satellite experiencing a thermal fluctuation and a signal transmission delay respectively. It is known that
P(A)=0.3P(A∪B)=0.58 P(A) = 0.3 \quad P(A \cup B) = 0.58 P(A)=0.3P(A∪B)=0.58Given that A A\,A and B B\,B are independent,
show that P(B)=0.4P(B) = 0.4P(B)=0.4
(4)
The event C C\,C represents a specific sensor failure that is known to occur only during thermal fluctuations, such that
P(C)=0.12P(A∩C)=P(C) P(C) = 0.12 \quad P(A \cap C) = P(C) P(C)=0.12P(A∩C)=P(C)Find P(C′∣A)P(C' | A)P(C′∣A)
(2)
Given that B B\,B and C C\,C are mutually exclusive,
draw a Venn diagram to represent the events AAA, B B\,B and CCC, giving the exact probabilities of each region in the Venn diagram.
(5)
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.