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I\'ve put this question on before, but whoever answered got it wrong. Please onl

ID: 2958230 • Letter: I

Question

I've put this question on before, but whoever answered got it wrong. Please only answer if you know the correct answer and can explain. Thanks!

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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