Question

Problem 8. Edward's experience shows that 7% of the parcels he mails will not reach their destination. He has bought two books for $20 each and wants to mail them to his brother. If he sends them in one parcel, the postage is $5.20, but if he sends them in separate parcels, the postage is $3.30 for each book. To minimize the expected value of his expenses (loss + postage), which way is preferable to send the books, as two separate parcels or as a single parcel?

Answer 1

Anscuess! The probability that the parcels will not seach thier destination is 74 20.07. PP 1-0.07 20.93 compute the first, notice, when the parrel reaching its destination a "success and not reaching its destination a "failure". €(x) = np The scuress" probability is pand payoffs ase $5.20 upon sucess 2x $ 20 + $5-20 - $45:50 Expected cost : Elipoce); s 2xP+(1045) = 45.20-hop = 45.20-6060 -93) - $8.00 (1-P) cohen sending tovo parcels, binomial sandam veniable arith two toials p=0.93 & payoff $3.30 when a single trial succeds & $20 + $ 6.60 = $26.60 when cs single foils fails. CamScanner

- probability and payoffs for two tsails are shown below cost case probability 0 2 Successes (both parcels reach) :$6.60 2) I successes (one of the two parcels reaches) (2) Pl(1-P) I $ 204 86.60 - $26.60 $20 + $26.60 = $46.60 o successes (neither parcel reaches) The expected cost is € (z pacels) = 660%(9) P?CO-PY] 426 60*[C) p'ı-p"} +46 0[(8) p2 (1-] • 660 xp2 + 26-60x2P(1-P) +4660x(1-P)2 = 66 6-hop since p=0.93, then E (a paocels) - 46.60 -40 (0-93) 66 60 37.2 < $9.46 henre The qiven expected costs, it's betteo to send one more than twoth CScanScanner