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 (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.