Question

A survey of homes in a particular suburb showed that in the past five years 30% installed solar panels, 60% added more insulation, and 25% did both.

a. What does the proper Venn diagram look like?

b. What percentage of homes in this suburb did at least one of these two things?

c. What percentage of homes did only one of these things?

d. A randomly selected home has new solar panels. What is the probability that it also has new insulation?

e. Are installing solar panels and adding more insulation disjoint events? Explain briefly.

Answer 1

S = Solar panel

I = New insulation

(a) Venn diagram

(b) P( home that did atleast one things) = Did one thing + Did both the things

P( home that did atleast one things) =  0.05 + 0.35 + 0.25 = 0.65

Percentage of home that did atleast one things = 65%

(c) P(home that did only one things) = 0.05 + 0.35 = 0.40

Percentage of home that did only one things = 40%

(d) P(I / S) = P(I S) / P(S) = 0.25 / 0.30 = 0.833

P(I / S) = 0.833

(e) Installing solar panels and adding more insulation are NOT disjoint events. Two set are disjoint if there is no element in common, i.e.  P(I S) =0 . Bue here  P(I S) = 0.25

hence  installing solar panels and adding more insulation are not disjoint.