A certain company sends 40% of its overnight mail parcels via express mail servi

Question

A certain company sends 40% of its overnight mail parcels via express mail service El. of these parcel, 2% arrive after the guaranteed delivery time (denote the event "late delivery" by L). Suppose that 50% of the overnight parcels are sent via E2 and the rem aining 10% sent via express mail service E3. Of those sent via E2, only 1% arrive late, whereas 5% of the parcels handled by E3 arrive late. a) What is the probability that a randomly selected parcel went via E1 and was late b) What is the probability that a randomly selected parcel arrive late c) If a randomly selected parcel has arrived on time, what is the probability that it was not sent via El

Explanation / Answer

a) probability that parcel went via E1 and was late =P(E1)*P(L|E1) =0.4*0.02 =0.008

b)probability of late =P(L) =P(E1)*P(L|E1)+P(E2)*P(L|E2)+P(E3)*P(L|E3)=0.4*0.02+0.5*0.01+0.1*0.05=0.018

c) probability of arriving on time(T) =1-P(L) =1-0.018 =0.982

probability of not sending via E1 given arrive on time =1-P(sent via E1 given arrive on time)

=1-P(E1)*P(T|E1)/P(T) =1-0.4*0.98/0.982=0.6008

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