Question

There are three modes of transporting material from New York 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 bay highway and the rest is by rail shipments. The percentage of damaged cargo are, respectively. 10% by highway, 5% by rail, 6% by sea, and 2% by air. (a) What percentage of all cargos may be expected to be damaged

Answer 1

5.7%

Explanation:

% Prob (Land) = Half ie 50% ; % Prob (Sea) = 30%

% Prob (Air) = Remaining ie 100% - 50% - 30% = 20%

Prob (Land highway) = 40% of land = 40% of 50% = 20%

Prob (Land rail) = remaining ie 60% of land = 60% of 50% = 30%

Pr (Damage by Land) = 10% of rail + 5% of rail = 10% of 20% + 5% of 30% = 2% + 1.5% = 3.5%

Prob (Damage by Sea) = 6% of sea = 6% of 30% = 1.8%

Prob (Damage by Air) = 2% of air = 2% of 20% = 0.4%

Total Prob (Damage) = 3.5% + 1.8% + 0.4%

= 5.7%