In the language of government statistics, the "labor force" includes all civilians over 16 years of age who are working or looking for work. We select a member of the U. S. labor force at random, and let A be the event that the person selected is white, and let B be the event that he or she is employed. In 1995, 84.6% of the labor force was white. Of the whites in the labor force, 95.1% were employed. Among non-white members of the labor force, 91.9% were employed.
a) Express the percents given for each event as a probability.
b) Draw a tree diagram for recording first the race (white or non-white) of a randomly chosen member of the labor force and then whether or not the person was employed.
c) Find the probability that the person chosen is an employed white member.
d) Find the probability that an employed non-white member is chosen.
e) What is the probability P(B) that the person chosen is employed?