- A factory produces shoes.
A quality control inspector at the factory checks a sample of 120 shoes for each of three types of defect. The Venn diagram represents the inspector's results.
A represents the event that a shoe has defective stitching \(B\) represents the event that a shoe has defective colouring \(C\) represents the event that a shoe has defective soles
\includegraphics[max width=\textwidth, alt={}, center]{fa1cb8a2-dab9-4133-b7a1-9108888c37d7-02_684_935_607_566}
One of the shoes in the sample is selected at random.
- Find the probability that it does not have defective soles.
- Find \(\mathrm { P } \left( A \cap B \cap C ^ { \prime } \right)\)
- Find \(\mathrm { P } \left( A \cup B \cup C ^ { \prime } \right)\)
- Find the probability that the shoe has at most one type of defect.
- Given the selected shoe has at most one type of defect, find the probability it has defective stitching.
The random variable \(X\) is the number of the events \(A , B , C\) that occur for a randomly selected shoe.
- Find \(\mathrm { E } ( X )\)
\section*{This is a copy of the Venn diagram for this question.}
\includegraphics[max width=\textwidth, alt={}, center]{fa1cb8a2-dab9-4133-b7a1-9108888c37d7-05_684_940_388_566}