There are three modes of transporting material from Ontario to Florida, namely,

Question

There are three modes of transporting material from Ontario to Florida, namely, by land, sea, or air. Also land transportation may be by rail or highway. About half of the materials are transported by land, 30% by sea, and the rest by air. Also, 40% of all land transportation is by highway and the rest by rail shipments. The percentages of damaged cargo are, respectively, 10% by highway, 5% by rail, 6% by sea, and 2% by air. (1) (2) What percentage of all cargoes may be expected to be damaged? If a damaged cargo is received, what is the probability that it was shipped by land? By sea? By air?

Explanation / Answer

P(shipped by land) = 0.5

P(shipped by sea) = 0.3

P(shipped by air) = 0.2

P(shipped by highway | shipped by land) = 0.4

P(shipped by highway) = P(shipped by highway | shipped by land) * P(shipped by land) = 0.4 * 0.5 = 0.2

P(shipped by rail | shipped by land) = 1 - 0.4 = 0.6

P(shipped by rail) = P(shipped by rail | shipped by land) * P(shipped by land) = 0.6 * 0.5 = 0.3

1) P(damage | shipped by highway) = 0.1

P(damage | shipped by rail) = 0.05

P(damage | shipped by sea) = 0.06

P(damage | shipped by air) = 0.02

P(damage) = P(damage | shipped by highway) * P(shipped by highway) + P(damage | shipped by rail) * P(shipped by rail) + P(damage | shipped by sea) * P(shipped by sea) + P(damage | shipped by air) * P(shipped by air)

                   = 0.1 * 0.2 + 0.05 * 0.3 + 0.06 * 0.3 + 0.02 * 0.2

                   = 0.057 (ans)

2) P(shipped by highway | damage) = P(damage | shipped by highway) * P(shipped by highway) / P(damage) = 0.1 * 0.2 / 0.057 = 0.351

P(shipped by rail | damage) = P(damage | shipped by rail) * P(shipped by rail) / P(damage) = 0.05 * 0.3 / 0.057 = 0.263

P(shipped by land | damage) = P(shipped by highway | damage) + P(shipped by rail | damage) = 0.351 + 0.263 = 0.614 (ans)

P(shipped by sea | damage) = P(damage | shipped by sea) * P(shipped by sea) / P(damage) = 0.06 * 0.3 / 0.057 = 0.316 (ans)

P(shipped by air | damage) = P(damage | shipped by air) * P(shipped by air) / P(damage) = 0.02 * 0.2 / 0.057 = 0.07 (ans)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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