The masses of a specific breed of adult dog are normally distributed with a mean of 24 kg24\text{ kg}24 kg and a standard deviation of 5 kg5\text{ kg}5 kg.
Find the probability that a randomly selected dog from this breed has a mass greater than 31.5 kg31.5\text{ kg}31.5 kg.
Any dog of this breed with a mass greater than 31.5 kg31.5\text{ kg}31.5 kg is classified as "heavy".
A dog of this breed is chosen at random. Given that it is classified as heavy,
find the probability that it has a mass greater than 36 kg36\text{ kg}36 kg.
Among the heavy dogs, exactly 25%25\%25% have a mass greater than m kgm\text{ kg}m kg.
Find the value of mmm.
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.