A survey of 120 software developers was conducted to determine which programming languages they used for a specific project: Python (PPP), Java (JJJ), and C++ (CCC). The results were as follows:
Represent this information in a Venn diagram.
A developer is chosen at random from the survey group.
Calculate the probability that the developer used Java but did not use Python or C++.
Find the probability that the developer used Java or C++ or both.
Given that the developer used Java or C++ or both,
calculate the probability that the developer did not use Python.
Determine whether the events 'using Python' and 'using Java' are statistically independent. Justify your conclusion.
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.