The reliability of a deep-sea submersible is monitored via three independent systems. Let S S\,S be the event that the hull integrity sensor triggers an alarm, P P\,P be the event that the power supply stability module reports a fault, and C C\,C be the event that the communication array fails.
Historical data indicates that P(S)=0.35P(S) = 0.35P(S)=0.35, P(P)=0.45P(P) = 0.45P(P)=0.45, and P(S∩P)=0.14P(S \cap P) = 0.14P(S∩P)=0.14.
Determine the probability that the submersible experiences either a hull alarm or a power fault, P(S∪P)P(S \cup P)P(S∪P).
Calculate P(P′∣S′)P(P' | S')P(P′∣S′), the probability that the power supply is stable given that no hull alarm was triggered.
The probability of a communication failure is P(C)=0.20P(C) = 0.20P(C)=0.20.
It is known that the hull alarm and communication failure are mutually exclusive events, and the power supply module and communication array operate independently.
Find P(P∩C)P(P \cap C)P(P∩C).
Describe the configuration of a Venn diagram for events SSS, PPP, and CCC, and state the probabilities for each of the six distinct regions.
Find the probability that neither a power fault nor a communication failure occurs, P((P∪C)′)P((P \cup C)')P((P∪C)′).
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.