Based on a random sample of 500 married women, the following table gives the joint PMF of their work status in relation to the presence or absence of children in the household.10
CHILDREN AND WORK STATUS OF WOMEN IN THE UNITED STATES

a. Are children and working outside of the home mutually exclusive?
b. Are working outside of the home and presence of children independent events?

Works outside Does not work home 0.2 0,4 outside home 0.3 0.1 Total 0.5 0.5 Has children Does not have children Total 0.6 0.4 1.0