A survey of 80 software developers records the programming languages they use.
Of the 80 developers, 50 use Python, 32 use Java and 20 use both Python and Java.
One of the 80 developers is chosen at random. The event Y Y\,Y is defined as the developer uses Python, and the event J J\,J is defined as the developer uses Java.
Determine whether the events Y Y\,Y and J J\,J are independent. Fully justify your answer.
Find P(J∣Y)P(J \mid Y)P(J∣Y).
198 exam-style questions on AQA A Level Maths 2.3 M: Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Conditional probability (A-level only), 2.3.3 Modelling with probability (A-level only), and 2.3 M: Probability. Each one has a worked solution and a mark scheme showing where the marks go.