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
- Find the value of \(k\).
[0pt]
[1 mark]
11 - Find the probability that a customer, visiting Terence's shop during the spring, will find at least 2 checkouts staffed.
[0pt]
[2 marks]