- A company has 1825 employees.
The employees are classified as professional, skilled or elementary.
The following table shows
- the number of employees in each classification
- the two areas, \(A\) or \(B\), where the employees live
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | \(\boldsymbol { A }\) | \(\boldsymbol { B }\) |
| Professional | 740 | 380 |
| Skilled | 275 | 90 |
| Elementary | 260 | 80 |
An employee is chosen at random.
Find the probability that this employee
- is skilled,
- lives in area \(B\) and is not a professional.
Some classifications of employees are more likely to work from home.
- \(65 \%\) of professional employees in both area \(A\) and area \(B\) work from home
- \(40 \%\) of skilled employees in both area \(A\) and area \(B\) work from home
- \(5 \%\) of elementary employees in both area \(A\) and area \(B\) work from home
- Event \(F\) is that the employee is a professional
- Event \(H\) is that the employee works from home
- Event \(R\) is that the employee is from area \(A\)
- Using this information, complete the Venn diagram on the opposite page.
- Find \(\mathrm { P } \left( R ^ { \prime } \cap F \right)\)
- Find \(\mathrm { P } \left( [ H \cup R ] ^ { \prime } \right)\)
- Find \(\mathrm { P } ( F \mid H )\)
\includegraphics[max width=\textwidth, alt={}]{3a09f809-fa28-4b3d-bb69-ea074433bd8f-13_872_1020_294_525}
Turn over for a spare diagram if you need to redraw your Venn diagram.
Only use this diagram if you need to redraw your Venn diagram.
\includegraphics[max width=\textwidth, alt={}, center]{3a09f809-fa28-4b3d-bb69-ea074433bd8f-15_872_1017_392_525}