Question

The Bureau of the Census in the United States attempted to count every U.S. resident. Suppose that the counts in the table are obtained for four counties in one region. (Give all answers to four decimal places.)

County	Race/Ethnicity
	Caucasian	Hispanic	Black	Asian	American Indian
Monterey	163,000	140,000	25,000	39,000	5,000
San Luis Obispo	190,000	38,000	7,000	9,000	3,000
Santa Barbara	230,000	121,000	12,000	24,000	5,000
Ventura	430,000	231,000	19,000	50,000	8,000

C. If one Hispanic person is selected at random from this region, what is the estimated probability that the selected individual is from Ventura?

(e) If one person is selected at random from this region, what is the estimated probability that the person is either Asian or from San Luis Obispo County?


(f) If one person is selected at random from this region, what is the estimated probability that the person is Asian or from San Luis Obispo County but not both?


(g) If two people are selected at random from this region, what is the estimated probability that both are Caucasians?


(h) If two people are selected at random from this region, what is the estimated probability that neither is Caucasian?


(i) If two people are selected at random from this region, what is the estimated probability that exactly one is a Caucasian?


(j) If two people are selected at random from this region, what is the estimated probability that both are residents of the same county?


(k) If two people are selected at random from this region, what is the estimated probability that both are from different racial/ethnic groups?

Answer 1

unty	Race/Ethnicity
	Caucasian	Hispanic	Black	Asian	American
					Indian	total
Monterey	163,000	140,000	25,000	39,000	5,000	372,000
San Luis Obispo	190,000	38,000	7,000	9,000	3,000	247,000
Santa Barbara	230,000	121,000	12,000	24,000	5,000	392,000
Ventura	430,000	231,000	19,000	50,000	8,000	738,000
total	1,013,000	530,000	63,000	122,000	21,000	1,749,000

e) estimated probability that the person is either Asian or from San Luis Obispo County

=(122,000+247000-9000)/1749000 =0.2058

f)

estimated probability that the person is Asian or from San Luis Obispo County but not both

=(122,000+247000-2*9000)/1749000 =0.2007

g)

estimated probability that both are Caucasians =(1013000/1749000)*(1012999/1748999)=0.3355

h)

P( estimated probability that neither is Caucasian ) =(736000/1749000)*(735999/1748999)=0.1771

i)

estimated probability that exactly one is a Caucasian =2*(1013000/1749000)*(1-1013000/1748999)

=0.4875

j)

estimated probability that both are residents of the same county =0.2935

k)

estimated probability that both are from different racial/ethnic groups =0.5664