An analysis of a digital archive of ancient manuscripts reveals that 35% of the manuscripts are written in Latin. It is also found that 45\displaystyle \frac{4}{5}54 of the manuscripts in the archive contain hand-drawn illustrations. Of the manuscripts that contain hand-drawn illustrations, the probability that a randomly chosen manuscript is written in Latin is 0.3.
Find the probability that a manuscript chosen at random from the archive:
is written in Latin and contains hand-drawn illustrations.
is not written in Latin and does not contain hand-drawn illustrations.
Determine, giving your reason, whether or not the events 'written in Latin' and 'contains hand-drawn illustrations' are statistically independent.
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.