An automated manufacturing system monitors three specific types of production errors: Event DDD (calibration drift), Event SSS (sensor saturation), and Event MMM (mechanical misalignment).
The probabilities of these errors occurring in a single cycle are given by:
P(D)=0.3,P(S∣D)=0.4,P(D∪S)=0.58,P(M)=0.5 P(D) = 0.3, \quad P(S|D) = 0.4, \quad P(D \cup S) = 0.58, \quad P(M) = 0.5 P(D)=0.3,P(S∣D)=0.4,P(D∪S)=0.58,P(M)=0.5Events DDD and MMM are known to be mutually exclusive.
Find P(D∪M)P(D \cup M)P(D∪M).
Show that P(S)=0.4P(S) = 0.4P(S)=0.4.
Given also that events SSS and MMM are independent,
draw a Venn diagram to represent the events DDD, SSS and MMM, indicating the probability associated with each of the eight regions.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.