Two boxes, X X\,X and YYY, contain red, blue, and green pens. Box X X\,X contains 2 red pens, 5 blue pens, and 3 green pens. Box Y Y\,Y contains 6 red pens, 2 blue pens, and 2 green pens. Casey picks one pen at random from Box X X\,X and places it into Box YYY. Casey then picks one pen at random from Box YYY.
Draw a tree diagram to represent this information.
Find the probability that Casey picks two pens of the same colour.
Given that both pens are the same colour, find the probability they are both blue.
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.