1) A certain company sends 40% of its overnight mail parcels via express mail se

Question

1) A certain company sends 40% of its overnight mail parcels via express mail service E1, 50% via express mail service E2 and the remaining via E3. Of those sent via E1 2% arrive late, of those sent via E2 1% arrive late, whereas 5% of the parcels handled by E3 arrive late. A record of an overnight mailing is randomly selected from the company’s file,

a.       (10 points) what is the probability that the selected parcel arrived late?

b.      (10 points) what is the probability that the parcel went via E1 and was late?

c. (10 points) If the randomly selected parcel has arrived late, what is the probability that it was sent via E1?

Please show all work

Explanation / Answer

Ans:

Given that

P(E1)=0.4

P(E2)=0.5

P(E3)=1-0.4-0.5=0.1

P(late/E1)=0.02

P(late/E2)=0.01

P(late/E3)=0.05

a)

P(late)=P(late/E1)*P(E1)+P(late/E2)*P(E2)+P(late/E3)*P(E3)

=0.02*0.4+0.01*0.5+0.05*0.1=0.018

b)

P(E1 and late)=P(late/E1)*P(E1)=0.02*0.40=0.008

c)

P(E1/late)=P(late/E1)*P(E1)/P(late)=0.02*0.4/0.018=0.444

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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