What is the most common organic tea in the market?

A market researcher investigating consumers' preference for three brands of beverages: coffee, tea and cocoa?

• in a certain town gathered the following info. from a sample of 800consumers, 230 took coffee,245 took tea,325 took cocoa.30 took all the beverages, 70 took coffee& cocoa, 110 took coffee only and 185 cocoa only. 1.present the above in a venn diagram 2.find the number who took tea only. 3.the number who took coffee and tea only 4.the number who took tea and cocoa only 5.the number who took none of the beverages

• Answer:

  1. I cant really draw the venn diagram here but here is what it will look like. Three circles representing tea, coffea and cocoa. They will all intersect. The area of double instersection is where all three circles overlap. Area of all three overlap = 30 Total Coffee = 230 Total Cocoa = 325 Total Tea = 245 Area of cocoa and coffee intersecting (including all three overlap) = 70 Coffee without any overlap = 110 Cocoa without any overlap = 185 2. Area of Tea and Cocoa (only) Intersecting(excluding all three intersecting) = Total Cocoa - Only Cocoa - Cocoa and Coffee = 325 - 185 - 70 = 70 Area of Tea and Coffee (only) Intersecting(excluding all three intersecting) = Total Coffee - Only Coffee - Cocoa and Coffee = 230 - 110 - 70 = 50 Area of Only tea = Total Tea - All three - tea and coffee - tea and cocoa = 245 - 70 - 50 - 30 = 95 3. Tea and Coffe only = 50 4. Tea and Cocoa only = 70 5. No Beverage = Sample Space - Total Tea - Total Coffee - Total Cocoa + Tea and Coffee only + Cocoa and Tea only + COcoa and Coffee (including all three)= 800 - 245 - 230 - 325 + 70 + 50 + 70 = 190