The Bureau of the Census in the United States attempted to count every U.S. citi

Question

The Bureau of the Census in the United States attempted to count every U.S. citizen and every resident. Suppose that the counts in the table are obtained for four counties in one region. Use the given information to estimate some probabilities. (Round your answers to four decimal places.)

(a) If one person is selected at random from this region, what is the probability that the selected person is from Ventura County?


(b) If one person is selected at random from Ventura County, what is the probability that the selected person is Hispanic?


(c) If one Hispanic person is selected at random from this region, what is the probability that the selected individual is from Ventura?


(d) If one person is selected at random from this region, what is the probability that the selected person is an Asian from San Luis Obispo County?


(e) If one person is selected at random from this region, what is the 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 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 probability that both are Caucasians?


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


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


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


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

County Race/Ethnicity Caucasian Hispanic Black Asian American
Indian Monterey 163,000 139,000 25,000 40,000 4,000 San Luis Obispo 180,000 38,000 7,000 10,000 4,000 Santa Barbara 230,000 121,000 13,000 25,000 6,000 Ventura 430,000 232,000 19,000 60,000 8,000

Explanation / Answer

Following table shows the caculations:

(a)

Out of 1754000 persons, 749000 are from Ventura county so

P(ventura county) = 749000 / 1754000 = 0.4270

(b)

Out of 749000 person from Ventura county, 232000 are Hispanic so

P(Hispanic | Ventura) = 232000 / 749000 = 0.3097

(c)

Out of 530000 Hispanic persons, 232000 are from Ventura county so

P(Ventura | Hispanic) = 232000 / 530000 = 0.4377

(d)

Out of 1754000 persons, 10000 person are Asian from San Luis Obispo County so required probability is

P(Asian and San Luis County) = 10000 / 1754000 = 0.0057

County Race/Ethnicity Caucasian Hispanic Black Asian American Indian Total Monterey 163,000 139,000 25,000 40,000 4,000 371,000 San Luis Obispo 180,000 38,000 7,000 10,000 4,000 239,000 Santa Barbara 230,000 121,000 13,000 25,000 6,000 395,000 Ventura 430,000 232,000 19,000 60,000 8,000 749,000 Total 1,003,000 530,000 64,000 135,000 22,000 1,754,000

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