Tim Gan Math
Sign up free

Completing a tree for machine set-up and faulty components, a total probability and a reverse conditional probability

Completing a tree for machine set-up and faulty components, a total probability and a reverse conditional probability

11 marks

At the start of each shift, a machine in a factory is set up correctly with probability \(\dfrac56\). When the machine is set up correctly, the probability that a component it makes is faulty is \(\dfrac{1}{10}\). When it is not set up correctly, the probability that a component it makes is faulty is \(\dfrac25\). A component made during a randomly chosen shift is tested. Let \(C\) be the event that the machine was set up correctly for that shift and \(F\) the event that the component is faulty.

  1. Copy and complete the following tree diagram.[4]
________
\(C\)
________
\(C'\)
________
\(F\)
________
\(F'\)
________
\(F\)
________
\(F'\)
  1. Find the probability that the component is faulty.[3]
  2. Given that the component is faulty, find the probability that the machine was set up correctly.[4]

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create free accountSign inIB Math tuition

Create a free account to practise similar questions.

Create free accountSign inIB Math tuition
Answer:(a) \(P(C)=\dfrac56,\ P(C')=\dfrac16,\ P(F\mid C)=\dfrac{1}{10},\ P(F'\mid C)=\dfrac{9}{10},\ P(F\mid C')=\dfrac25,\ P(F'\mid C')=\dfrac35\) (b) \(\dfrac{3}{20}\) (c) \(\dfrac59\)

Need help? Join our JC Math tuition classes.

Learn more