A shopping company facilitates for customers the transfer ofany items from any l

Question

A shopping company facilitates for customers the transfer ofany items from any location to another within the US. Thecompany transfers 25, 50, and 25% of the items by air, ground, andsea transportation, respectively. Assume that 10% of theitems shipped by air get damaged during shipping, 15% of itemsshipped by ground get damaged during shippig, and 5% of the itemsshipped by sea get damaged during shipping. Determine thefollowing probabilities: a) the probability of receiving a damaged item sent by air,ground, or sea. b) If an item was received damage, the probability that it was sent by i) air, ii) by ground, and iii) by sea A shopping company facilitates for customers the transfer ofany items from any location to another within the US. Thecompany transfers 25, 50, and 25% of the items by air, ground, andsea transportation, respectively. Assume that 10% of theitems shipped by air get damaged during shipping, 15% of itemsshipped by ground get damaged during shippig, and 5% of the itemsshipped by sea get damaged during shipping. Determine thefollowing probabilities: a) the probability of receiving a damaged item sent by air,ground, or sea. b) If an item was received damage, the probability that it was sent by i) air, ii) by ground, and iii) by sea

Explanation / Answer

bayer's rule      P(A /B)=       P(B/A) P(B)over   P(B/A) P(B) + P(B/A*)P(A*) air =25%    ground = 50% sea =25% 10% get damaged from air = 0.1 15% get damaged from ground=0.15 5% get damaged from sea=0.05 (a)    binomial therom (b)    bayer'srule        A is the prob sentby air and B is the prob it was damaged so by rule P(0.25/0.1) = (0.1)(0.25) over(0.1)(0.25)+(0.15)(0.5)+(0.25)(0.05)

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