Question

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?

Answer 1

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.