A high-precision manufacturing plant uses two independent-looking monitoring systems, Alpha and Beta, to detect micro-faults during production. Let AAA be the event that system Alpha flags a defect and BBB be the event that system Beta flags a defect. During a routine audit, the following probabilities were established:
P(A)=0.25,P(A∩B)=0.05andP(A′∩B′)=0.68 P(A) = 0.25, \quad P(A \cap B) = 0.05 \quad \text{and} \quad P(A' \cap B') = 0.68 P(A)=0.25,P(A∩B)=0.05andP(A′∩B′)=0.68Calculate the probability that for a single production unit:
At least one of the monitoring systems flags a defect.
System Beta flags a defect.
Given that system Alpha flags a defect, determine the probability that system Beta also flags it.
A quality control engineer suspects that the triggering of system Beta is linked to the performance of system Alpha. Determine whether or not events AAA and BBB are statistically independent.
Comment on the engineer's suspicion in light of your answer to part (d).
111 exam-style questions on WJEC A Level Maths 4.1.1 Probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.