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 41% of adults regularly recycle aluminum cans and believe that plastic, noncompostable shopping bags should be banned. In addition, suppose that 70% 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?

(Round your answers to 4 decimal places.)

Explanation / Answer

Let A = adult recycles, B = believes in ban

P(B) = 0.54
P(A and B) = 0.41
P(A|~B) = 0.7

a) P(A and ~B) = P(A|~B) x P(~B) = 0.7*(1-0.54) = 0.3220

b) P(A) = P(A|B) x P(B) + P(A|~B) x P(~B) = P(A and B) + P(A and ~B)
P(A) = 0.41 + 0.332 = 0.732

c) P(A or B) = P(A) + P(B) - P(A and B) = 0.732 + 0.54 - 0.41 = 0.862

d) P(~A or ~B) = P(~A) + P(~B) - P(~A and ~B)
P(~A and ~B) = 1 - P(A or B) = 1-0.862 = 0.138
P(~A or ~B) = P(~A) + P(~B) - P(~A and ~B) = 0.268 + 0.46 - 0.138 = 0.59

e) P(~B|A) = P(A and ~B)/P(A) = 0.332/0.732 = 0.45355 = 0.4536

Please rate my solution

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.