The 2010 American Community Survey estimates that 146 of Ame

The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English at home, and 4.2% fall into both categories. Answer the following questions:

If I choose two Americans at random, what is the probability that both live below the poverty line?

If I choose two Americans at random, what is the probability that both speak English at home?

Solution

Let

P = below poverty
L = does not speak English

a)

If I choose two Americans at random, what is the probability that both live below the poverty line?

P(both P) = 0.146*0.146 = 0.021316 [ANSWER]

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b)

If I choose two Americans at random, what is the probability that both speak English at home?

P(both L\') = (1-0.207)*(1-0.207) = 0.628849 [ANSWER]