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”.

(a) 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?

(b) 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 $3, 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

a) Geometric Distribution the probability 1- the propabily to won in the first, second, third, and fourth day

0.05+0.05*0.95+0.05*0.95*0.95+0.05*0.95*0.95*0.95=0.18549

1-0.18549=0.8145

b) Binomial Distribution

P(1)=C(10,1)*(0.05^(1))*(0.95^(10-1))=0.3151

The A has to go 8 times to get the same probability of B so hi has to pay in transportation cost 8 times and $24 for 8 boxes, in other way B only has to pay one time the transportation cost and $30 for the 10 boxes so its better the strategy of A if the transportation cost is $0.86 or less if not the strategy B is the best

x+30=8*x+24

x=$0.86

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