12   5. 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 A B Professional 740 380 Skilled 275 90 Elementary 260 80 An employee is chosen at random. Find the probability that this employee (a) is skilled, (1) (b) lives in area B and is not a professional. (1) 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 (c) Using this information, complete the Venn diagram on the opposite page. (4) (d) Find P (R' ∩ F) (1) (e) Find P ([H ∪ R]' ) (1) (f) Find P (F | H ) (2) _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 13   Question 5 continued H R F 123 133 247 412 Turn over for a spare diagram if you need to redraw your Venn diagram. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________