The following table gives the percentages of men and women 20 years and older employed in various occupations in the U.S. workforce in 2010, from the Current Population Survey. Each column sums to 100%. There are about 70 million men and 70 million women in the workforce.

(a) The number 14 in the second row of the table, after dividing by 100, represents which of these: P (Man and Service), P(Man | Service), P(Man) * P(Service), P(Service | Man).
(b) If you pick a person at random from the sales and office occupations, what is the probability you picked a woman?
(c) If you know someone€™s occupation, can you guess whether they are male or female? Which occupation makes this guess easiest? Hardest?
(d) What is the probability of picking someone at random from the service industry?

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Sex Men Womern Management & Professional Service Sales & Office 35 14 17 42 20 32 Occupation Mining & Construction Production & Transportation Total 17 17 100% 100%