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

Question

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% of the items shipped by ground get damaged during shipping, and 15% of the items shipped by sea get damaged during shipping. Determine the following probabilities: 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

A)

Let

D= damaged

A, G, S = air, ground, sea

Hence,

P(D) = P(A) P(D|A) + P(G) P(D|G) + P(S) P(D|S)

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

P(D) = 0.105 [ANSWER]

******************

b)

i)

P(A|D) = P(A) P(D|A) / P(D) = 0.20*0.05/0.105 = 0.095238 [ANSWER]

ii)

P(G|D) =P(G) P(D|G)/P(D) = 0.50*0.10/0.105= 0.47619 [ANSWER]

iii)

P(S|D) = P(S) P(D|S) / P(D) = 0.30*0.15/0.105 = 0.428571 [ANSWER]

*****************

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.