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 A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.