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)
198 exam-style questions on AQA A Level Maths 2.3 M: Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Conditional probability (A-level only), 2.3.3 Modelling with probability (A-level only), and 2.3 M: Probability. Each one has a worked solution and a mark scheme showing where the marks go.