Two jars, J1 J_1\,J1 and J2J_2J2, contain blue, white, and black marbles. Jar J1 J_1\,J1 contains 4 blue marbles, 3 white marbles, and 3 black marbles. Jar J2 J_2\,J2 contains 2 blue marbles, 5 white marbles, and 1 black marble. Sam picks one marble at random from jar J1 J_1\,J1 and places it into jar J2J_2J2. Sam then picks one marble at random from jar J2J_2J2.
Draw a tree diagram to represent this information.
Find the probability that Sam picks two marbles of the same colour.
Given that both marbles are the same colour, find the probability they are both black.
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.