In each round of a game, a player scores 2 points with probability 0.30, 1 point with probability 0.50, and 0 points otherwise. The scores in two rounds are independent.
Find the probability that the player's total score is at least 3.
In 400 pairs of rounds, find the expected number for which the total score is at least 3.
Give one reason why the independence assumption might not hold in practice.
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.