7 At a factory that makes crockery the quality control department has found that \(10 \%\) of plates have minor faults. These are classed as 'seconds'. Plates are stored in batches of 12. The number of seconds in a batch is denoted by \(X\).
- State an appropriate distribution with which to model \(X\). Give the value(s) of any parameter(s) and state any assumptions required for the model to be valid.
Assume now that your model is valid.
- Find
(a) \(\mathrm { P } ( X = 3 )\),
(b) \(\mathrm { P } ( X \geqslant 1 )\). - A random sample of 4 batches is selected. Find the probability that the number of these batches that contain at least 1 second is fewer than 3 .