Question

cannot occur at the same me 050 auct women more likely to be unemployed than men? The following table pron employment status of the U.S. population, 16 years of Is in thousands of people. (Source: Bureau of Labor Statistics.) Population, 16 years of age and older in the labor force as of October 2012. The data following table provides data on the gender and Total Men Women 76,055 Employed 143,384 67,329 Unemployed 6,642 5,616 12,258 Total 82,697 72,945 155,642 What is the probability that a randomly selected person: a. Is unemployed given that she is a woman? b. Is unemployed given that he is a man?

Answer 1

From the given data,

a. Probability that a randomly selected person is unemployed given that she is women is,

P( unemployed | Women) = P( Unemployed women)/ P( Women)

$\\ P( unemployed\: |\: Women) = \frac{5616/155642}{12258/155642} \\ \\ P( unemployed\: |\: Women) = \frac{5616}{12258} \\ \\ P( unemployed\: |\: Women) = \frac{104}{227} \\ \\ P( unemployed\: |\: Women) = 0.45815$

Therefore,

Probability that a randomly selected person is unemployed given that she is women is 0.45815

b) Probability that a randomly selected person is unemployed given that he is men is,

P( unemployed | men) = P( Unemployed men)/ P( men)

$\\ P( unemployed\: |\: men) = \frac{6642/155642}{12258/155642} \\ \\ P( unemployed\: |\: men) = \frac{6642}{12258} \\ \\ P( unemployed\: |\: men) = \frac{123}{227} \\ \\ P( unemployed\: |\: men) = 0.54185$

Probability that a randomly selected person is unemployed given that he is men is 0.54185.

c) Here probability of unemployment in men (0.54185) is more than probability of unemployment in women (0.45815)

Thus , We can not say that women are more likely than men to be unemployed.