A retail study by Deloitte revealed that 54% of adults surveyed believed that pl

Question

A retail study by Deloitte revealed that 54% of adults surveyed believed that plastic, noncompostable shopping bags should be banned. Suppose 42% of adults regularly recycle aluminum cans and believe that plastic, noncompostable shopping bags should be banned. In addition, suppose that 60% of adults who do not believe that plastic, noncompostable shopping bags should be banned do recycle. If an adult is randomly selected,

a. What is the probability that the adult recycles and does not believe that plastic, noncompostable shopping bags should be banned?

b. What is the probability that the adult does recycle?

c. What is the probability that the adult does recycle or does believe that plastic, noncompostable shopping bags should be banned?

d. What is the probability that the adult does not recycle or does not believe that plastic, noncompostable shopping bags should be banned?

e. What is the probability that the adult does not believe that plastic, noncompostable shopping bags should be banned given that the adult does recycle?

Explanation / Answer

a) here probabilty of person who thinlks that it should be banned=P(B)=0.54

and not banned=P(NB)=0.46

probabilty of those who recycle and think need to be banned=P(R&B)=0.42

recycle but do not believe =P(R|NB)=0.6

a) probability that the adult recycles and does not believe that plastic =P(R&NB)=P(NB)*P(R|NB)=0.46*0.6=0.276

b) probability that the adult does recycle=P(R)=P(B)*P(R|B)+P(NB)*P(R|NB)=0.42+0.276=0.696

c)probability that the adult does recycle or does believe that plastic, noncompostable shopping bags should be banned =P(R UB)=P(R)+P(B)-P(R&B)=0.696+0.52-0.42=0.796

d)probability that the adult does not recycle or does not believe that plastic, noncompostable shopping bags should be banned =P(RcUBc) =P(R&B)c =1-P(R&B)=1-0.42=0.58

e)probability that the adult does not believe that plastic, noncompostable shopping bags should be banned given that the adult does recycle =P(NB|R) =P(NB)*P(R|NB)/P(R)=0.276/0.696=0.3966

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