Conditional probability or memoryless

A question is this type if and only if it asks to find conditional probabilities given that a component has already lasted a certain time, using the memoryless property.

1 questions

AQA Further Paper 3 Statistics Specimen Q8
9 marks
8 The time in hours to failure of a component may be modelled by an exponential distribution with parameter \(\lambda = 0.025\) In a manufacturing process, the machine involved uses one of these components continuously until it fails. The component is then immediately replaced.
8
  1. Write down the mean time to failure for a component. 8
  2. Find the probability that a component will fail during a 12-hour shift. 8
  3. A component has not failed for 30 hours. Find the probability that this component lasts for at least another 30 hours.
    [0pt] [2 marks] 8
  4. Find the probability that a component does not fail during 4 consecutive 12-hour shifts.
    [0pt] [3 marks]
    8
    1. State the distribution that can be used to model the number of components that fail during one hour of the manufacturing process.
      [0pt] [2 marks]
      8
  6. (ii) Hence, or otherwise, find the probability that no components fail during 5 consecutive 12-hour shifts.
    [0pt] [2 marks]