Selected boxes of breakfast cereal contain a prize. Suppose that 5% of the boxes

Question

Selected boxes of breakfast cereal contain a prize. Suppose that 5% of the boxes contain the prize and the other 95% contain the message "Sorry, try again". Consumer A. only buys one box of cereal on a single visit to the grocery store. She decides to continue coming to the store and purchase boxes of cereal until she gets a prize. What is the probability that she will have to purchase more than 4 boxes of cereal until a prize is found? Consumer B decides to buy 10 boxes of cereal on a single visit to the same grocery store. Suppose the price of each box of cereal is S3, and the reward for getting a box that contains a prize is $80. We further assume that consumers incur a transportation cost every time they visit the grocery store. Which strategy has a better pay-off (consumer A's or consumer B s) depending on the value of the transportation cost per visit?

Explanation / Answer

1) Probability that the person A has to purchase more than four boxes

= 1 - P ( he wins in the first 4 trials)

= 1 - [ P(X=1) + P(X=2) + P(X=3) + P(X=4) ]

= 1 - [ (0.05) + (0.05*0.95) + (0.95 * 0.95 * 0.05) + (0.95*0.95*0.95*0.05) ]

= 1 - 0.1854

= 0.8146

81.46% chance that it will take more than 4 visits.

B)

Let 't' be the transportation cost per visit

Expected winning for A : (-0.95)(t+3) + (0.05)(80-3-t)

Expected winning for B : -(30 + t)(0.95)10 + (80 - 30 - t)[1 - (0.95)10 ]

Thus, better strategy depends upon the transportation costs.

Hope this helps.

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