A newsboy purchases 50 newspapers for 35 cents each and sells them for 60 cents

Question

A newsboy purchases 50 newspapers for 35 cents each and sells them for 60 cents each. He can return any unsold papers and recoup 25 cents for each. A total of 100 people pass by him each day, and each decides (independently of all other passers by) to ask to buy a paper with probability 0.6. (d) One day, after the newsboy has sold all of his papers, an angry customer demands a paper. After this experience, the newsboy decides to increase the number of papers he buys. Being fairly cautious, he decides to begin by buying one extra paper. i) What is the probability that he sells this extra paper? i) What is the average additional profit that he makes from this paper? (e) Encouraged by his success, on the next day he decides to buy 52 papers. i) What is the probability that he sells this extra paper (i.e., the 52nd paper)? ii) What is the average additional profit that he makes from this 52nd paper? iii) Is the average additional profit that from the 52nd paper larger or smaller than the average additional proft that from the 5 Ist paper?

Explanation / Answer

d) i) The probability that he sell this extra paper is 0.6

ii) If he sells the extra paper than he will make a profit of ( 60-35)=25 cents

if he cannot sell the extra paper than he will be in loss of (35-25) =10 cents

Hence on average, he will be 0.6*25-0.4*10=11 cents in profit

e) i) The probability that he sells this extra paper is 0.6

ii) the average additional profit that he makes from this 52nd paper is 0.11

iii)It is same

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