3. A shipping company facilitates for customers the transfer of any item s from

Question

3. A shipping company facilitates for customers the transfer of any item s from any location to anoth er 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% of the items shipped by ground get damaged uring shipping, and 15% of the items shipped by sea get dam aged during shipping. Determine the following probabilities: 50 40 30 20 n 10 Damaged Undamaged JO Air Ground Sea shipping methods 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(i) air, (ii) by ground, and (iii) by 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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