Question

Data was collected in a study of 5000 women designed to investigate married women's participation in the workplace. Consider the following experiment: select a random participant from the 5000 women in the study, and observe whether they work full-time (event F), part-time (event P) or do not have a paid job (event N). Also observe whether they have no children under 18 (event H), or at least one child under 18 (event C). Based on the results of this study, the probabilities of various events are summarised in the following contingency table.

	C	H
F	0.279	0.131
P	0.185	0.052
N	0.332	0.021

1. What method was used to obtain the probabilities in the table?
2. Complete the contingency table by supplying marginal probabilities (row and column totals).
3. Use the contingency table to find the probability that the chosen participant works full-time. Show your working.
4. What is the probability that she works full-time, given that she has at least one child under 18? Show your working.
5. Are events F and C are mutually exclusive. Briefly explain your decision.

Answer 1