AQA Paper 3 Specimen — Question 11 3 marks

Exam BoardAQA
ModulePaper 3 (Paper 3)
SessionSpecimen
Marks3
TopicDiscrete Probability Distributions
TypeOne unknown from sum constraint only

11 Terence owns a local shop. His shop has three checkouts, at least one of which is always staffed. A regular customer observed that the probability distribution for \(N\), the number of checkouts that are staffed at any given time during the spring, is $$\mathrm { P } ( N = n ) = \left\{ \begin{array} { c c } \frac { 3 } { 4 } \left( \frac { 1 } { 4 } \right) ^ { n - 1 } & \text { for } n = 1,2
k & \text { for } n = 3 \end{array} \right.$$ 11
  1. Find the value of \(k\).
    [0pt] [1 mark]
    11
  2. Find the probability that a customer, visiting Terence's shop during the spring, will find at least 2 checkouts staffed.
    [0pt] [2 marks]