Please show all your work. thanks in advance This is a written question, worth 1

Question

Please show all your work. thanks in advance

This is a written question, worth 15 points. DO NOT place the problem code on the answer sheet.A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit Problem Code: 962 A certain company sends 50% of its overnight mail parcels via express mail service El. of these parcels 1% amve after the guaranteed delivery time (denote the event late delivery by L). Suppose that 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sent via E3. of those sent via E2 on 2% amve late, whereas 5% of the parcels handled by E3 amve late. Part a: If a record of an ovenight mailing is randomly selected from the company's file, what is the probability that the parcel went via El and was late? Part b: What is the probability that a randomly selected parcel arrived late? Part e: If a randomly selected parcel has arrived on time, what is the probability that is was not sent via E1? a) Ihave placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.

Explanation / Answer

a)P(via E1 and late)=P(via E1)*P(late|via E1) =0.5*0.01=0.005

b)

P(late)=P(via E1)*P(late|via E1)+P(via E2)*P(late|via E2)+P(via E3)*P(late|via E3)

=0.5*0.01+0.1*0.02+0.4*0.05=0.027

c)

P(arrive on time)=1-P(late)=1-0.027 =0.973

P(not via E1|on time) =1-P(via E1|on time) =1-0.5*(1-0.01)/0.973=0.4913

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