A logistics operations analyst investigates parcels for two specific errors: Delayed Shipping (DDD) and Mislabeled Address (MMM). The probability that a parcel is delayed is 0.15. If a parcel is delayed, the probability that it is also mislabeled is 0.20. If a parcel is not delayed, the probability that it is mislabeled is 0.06.
Construct a tree diagram to represent this information, including all branch probabilities for DDD and MMM.
Find the probability that a randomly selected parcel has exactly one of these two errors: Delayed Shipping or a Mislabeled Address.
The analyst also notes that a parcel can suffer External Damage (EEE) with a probability of 0.10, and this flaw is independent of shipping delays or labeling errors.
Determine the probability that a randomly selected parcel has none of these three flaws.
Calculate the probability that a randomly selected parcel has exactly one of these three flaws.
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.