Question

The contingency table below summarizes a survey of 1,000 bottled beverage consumers.

	Lives in a state with a deposit law				Lives in a state with no deposit law				Row Total
Recycles beverage bottles		137				180				317
Does not recycle beverage bottles		60				623				683
Column Total		197				803				1,000

Find the following probabilities or percentages:

(a) Probability that a consumer recycles beverage bottles. (Round your answer to 2 decimal places.)

P(Recycles)              

(b) Probability that a consumer who lives in a state with a deposit law does not recycle. (Round your answer to 2 decimal places.)

P(Don’t Recycle | Lives in Deposit Law State)              

(c) Percentage of consumers who recycle and live in a state with a deposit law. (Round your answer to 1 decimal place.)

Percentage of consumers              %

(d) Percentage of consumers in states with a deposit law who recycle. (Round your answer to the nearest whole percent.)

Percentage of consumers              %

Answer 1

From the provided table:

a) Probability that a consumer recycles beverage bottles is

P(Recycles)   =317/100=0.317

i.e P(Recycles) =0.32

Since there are total 317 consumer who recycles beverage bottles out of 1000 consumers.

b) Probability that a consumer who lives in a state with a deposit law does not recycle is;

P(Don’t Recycle | Lives in Deposit Law State) =60/197

P(Don’t Recycle | Lives in Deposit Law State) = 0.3045

P(Don’t Recycle | Lives in Deposit Law State) =0.30

c) Percentage of consumers who recycle and live in a state with a deposit law is:

Percentage of consumers =(137/1000)*100

Percentage of consumers =13.7%

d) Percentage of consumers in states with a deposit law who recycle is:

Percentage of consumers =(137/1000)*100

Percentage of consumers =13.7%

Percentage of consumers =14%