23. A shipping company facilitates for customers the transfer of any items from

Question

23. A shipping company facilitates for customers the transfer of any items from any location to another within the United States. The company transfers 20, 50, and 30% of the items by air, ground, and sea transportation, respectively. The breakdown of these items by shipping method is shown in the accompanying figure. Assume that 5% of the items shipped by air get damaged during shipping 10% NT 110 PROBABILITY, STAT ISTICS, AND RELIABILITY FOR ENGINEERS AND SCIE get damagedduring by ground get damaged during shipping, and 15% of the items shipped ng. Determine the following probabilities: Damaged 50 40 30 20 10 0 Undamaged Sea Ground shipping methods Air a. The probability of receiving a damaged item sent by air, ground, or sea b. If an item was received damaged, the probability that it was sent by (6) air, (ii) by ground, and (ii) sea

Explanation / Answer

P(receiving item by air) = 0.20

P(receiving item by ground) = 0.50

P(receiving item by sea) = 0.30

P(damage if received by air) = 0.20*0.05

P(damage if received by ground) = 0.50*0.10

P(damage if received by sea) = 0.30*0.15

a)

P(receiving a damaged item by air or ground or sea)

= P(damage if received by air) + P(damage if received by ground) + P(damage if received by sea)

= 0.20*0.05 + 0.50*0.10 + 0.30*0.15

=0.105

b)

P(item received by air/ item is damaged)

= P(damage through air)/P(P(receiving a damaged item by air or ground or sea)

= 0.20*0.05 / 0.105

= 0.095

P(item received by ground/ item is damaged)

= P(damage through ground)/P(P(receiving a damaged item by air or ground or sea)

= 0.50*0.10 / 0.105

= 0.476

P(item received by sea/ item is damaged)

= P(damage through sea)/P(P(receiving a damaged item by air or ground or sea)

= 0.30*0.15 / 0.105

= 0.429

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