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MathematicsMathematics
6 January, 11:31

According to the U. S. Census Bureau, the prob ability that a randomly selected household speaks only English at home is 0.81. The probability that a randomly selected household speaks only Spanish at home is 0.12. (a) What is the probability that a randomly selected household speaks only English or only Spanish at home? (b) What is the probability that a randomly selected household speaks a language other than only English or only Spanish at home? (c) What is the probability that a randomly selected household speaks a language other than only English at home? (d) Can the probability that a randomly selected household speaks only Polish at home equal 0.08? Why or why not?

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  1. 6 January, 11:47
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    Step-by-step explanation:

    Given that according to the U. S. Census Bureau, the prob ability that a randomly selected household speaks only English at home is 0.81.

    The probability that a randomly selected household speaks only Spanish at home is 0.12.

    (a) the probability that a randomly selected household speaks only English or only Spanish at home

    = 0.81+0.12 = 0.93

    (since these two are disjoint sets)

    (b) the probability that a randomly selected household speaks a language other than only English or only Spanish at home

    = 1-0.93 = 0.07 (remaining)

    (c) the probability that a randomly selected household speaks a language other than only English at home

    =1-0.81=0.19

    (d) Can the probability that a randomly selected household speaks only Polish at home equal 0.08? Why or why not?

    Polish alone can never exceed 1 - (0.81+0.12) i. e. 0.70

    At most it can take values as 0.7 only

    So no is the answer.
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