2) In the language of government statistics, the \"labor force\" includes all ci

Question

2) In the language of government statistics, the "labor force" includes all civilians at least 16 years of age who are working or looking for work. Select a member of the U.S. labor force at random. Suppose that 84.6% of the labor force is white. Of the Whites in the labor force, 95.1% are employed . Among nonwhite members of the labor force, 91.9% are employed. a. Find the probability that the person chosen is an employed white   

b. Out of the non-whites, what percentage is unemployed?

c. Find the probability that the person chosen is employed.

d. If someone is not employed, what is the probability that they are white?

In the language of government statistics, the "labor force" includes all civilians at least 16 years of age who are working or looking for work. Select a member of the U.S. labor force at random. Suppose that 84.6% of the labor force is white. Of the Whites in the labor force, 95.1% are employed. Among nonwhite members of the labor force, 91.9% are employed. a. Find the probability that the person chosen is an employed white Out of the non-whites, what percentage is unemployed? Find the probability that the person chosen is employed. If someone is not employed, what is the probability that they are white?

Explanation / Answer

here given that 84.6% of the labor force is white

that probability of labor force of white is 0.846

and probability of laabor force of non white is 1-0.846=0.154

and in white labor force probability of employed is 0.951

and probability of unemployed is 1-0.951=0.049

and in non white labor force probability of employeed is 0.919

and probability of unemployed is 1-0.911=0.081

a) now we have to find the probability that person chosen is employed white

=p( white/employed)

=p(white)*P(employed/white)/{(p(white)*P(employed/white)+p( non white)*P(employed/ non white)}

=0.951*0.846/(0.951*0.846+0.154*0.919)

=0.8045/0.9460

=0.8504

b) out of non white percentage of unemployed is

p(non white /unemployed)

=p(non white)*P(unemployed/non white)/{p(non white)*P(unemployed/non white)+P(white)*P(unemployed/white)

=0.081*0.154/{(0.081*0.154)+(0.846+0.049)}

=0.0125/0.54

=0.2315

c) now we have to find the probability that the person chosen is employed

=p(employed)

=p(white)*P(employed/white)+P(non white)*P(employed/non white)

=0.846*0.951+0.154*0.919

=0.9460

d) now we have to find the probability that the if someone is not employed that they are white

= p(white/unemloyed)

=p(unemployed/white)*P(white)/{P((unemployed/white)*P(white)+P(unemployed/non white )*P(non white)}

=0.049*0.846/{0.049*0.846+0.081*0.155}

=0.0415/0.05397

=0.769

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