Edexcel S1 2014 June — Question 4

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicTree Diagrams
TypePopulation partition tree diagram

  1. In a factory, three machines, \(J , K\) and \(L\), are used to make biscuits.
Machine \(J\) makes \(25 \%\) of the biscuits. Machine \(K\) makes \(45 \%\) of the biscuits. The rest of the biscuits are made by machine \(L\).
It is known that \(2 \%\) of the biscuits made by machine \(J\) are broken, \(3 \%\) of the biscuits made by machine \(K\) are broken and 5\% of the biscuits made by machine \(L\) are broken.
  1. Draw a tree diagram to illustrate all the possible outcomes and associated probabilities. A biscuit is selected at random.
  2. Calculate the probability that the biscuit is made by machine \(J\) and is not broken.
  3. Calculate the probability that the biscuit is broken.
  4. Given that the biscuit is broken, find the probability that it was not made by machine \(K\).