Mathematical Methods · Unit 1 · Probability · Language of events and sets
AI-marked practice questions tied to QCAA mark schemes for this exact LO. Free to start.
Start free practiceFull questions, answers and worked solutions unlock when you start a free practice session.
A café offers three sizes of coffee (small, medium, large) and four types of milk (full cream, skim, soy, almond). A customer selects one size and one type of milk. Describe the sample space for this selection process using set notation.
A student conducts an experiment by rolling a fair six-sided die and then spinning a spinner divided into three equal coloured sections: red, blue and yellow. (a) State the sample space for this combined experiment. (1 mark) (b) Use set notation to list all outcomes where the result is a number less than 4 on the die OR the spinner lands on red. (2 marks)
A factory quality control process inspects three consecutive items coming off a production line. Each item can either pass (P) or fail (F) the inspection. (a) List all possible outcomes in the sample space for this inspection process. (1 mark) (b) Define event \(A\) as 'exactly two items pass inspection' and express \(A\) as a set of outcomes. (1 mark) (c) Define event \(B\) as 'at least two consecutive items have the same result'. Express \(B\) as a set of outcomes. (1 mark) (d) Use your answers from parts (b) and (c) to determine the number of outcomes in the event \(A \cap B\). (1 mark)