The US Energy Department states that 60% of all US households have ceiling fans.

Question

The US Energy Department states that 60% of all US households have ceiling fans. In addition, 29% of all US households have an outdoor grill. Suppose 13% of all US households have both a ceiling fan and an outdoor grill. A US household is randomly selected.
a) What is the probability that the household has a ceiling fan or an outdoor grill?
b) What is the probability that the household has neither a ceiling fan nor an outdoor grill?
c) What is the probability that the household does not have a ceiling fan and has an outdoor grill?
d) What is the probability that the household does have a ceiling fan and does not have an outdoor grill?

Explanation / Answer

P(fans)=P(f)=0.6 P(grill)=p(g)=0.29 P(both)=0.13 -------------------------------------------------------------------------------------- a. What is the probability that the household has a ceiling fan or an outdoor grill? P(f or g)= P(f) +P(g)-P(both) =0.6+0.29-0.13 =0.76 -------------------------------------------------------------------------------------------- b. What is the probability that the household has neither a ceiling fan nor an outdoor grill? P(f' and g')= 1-P(f or g)=1-0.76= 0.24 -------------------------------------------------------------------------------------------- c.What is the probability that the household does not have a ceiling fan and does have an outdoor grill? P(f' and g)=P(g)-P(f and g) =0.29-0.13 =0.16 -------------------------------------------------------------------------------------------- d. What is the probability that the household does have a ceiling fan and does not have an outdoor grill? P(f and g') = P(f)-P(f and g) =0.6-0.13 =0.47

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