A football team either wins, draws or loses a match, with probabilities ppp, 0.20 and 0.80−p0.80-p0.80−p respectively. Results of two matches are modelled as independent. The probability of at least one win in the two matches is 0.51.
Find ppp.
The team earns 3 points for a win and 1 point for a draw. Find the probability that it earns exactly 4 points from the two matches.
In 250 pairs of matches, find the expected number in which the team earns exactly 4 points.
Give one reason why the results of consecutive matches may not be 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.