A certain company sends 40% of its overnight mail parcels by means of express ma
ID: 3058543 • Letter: A
Question
A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 4% arrive after the guaranteed delivery time.
Suppose that 50% of the overnight parcels are sent by means of express mail service A2 and the remaining 10% are sent by means of A3. Of those sent by means of A2, only 1% arrived late, whereas 5% of the parcels handled by A3 arrived late.
(a)What is the probability that a randomly selected parcel arrived late? (Hint: A tree diagram should help.)
(b) Suppose that a randomly selected overnight parcel arrived late. What is the probability that the parcel was shipped using mail service A1? That is, what is the probability of A1 given L, denoted P(A1|L)? (Round your answer to three decimal places.)
(c) What is P(A2|L)? (Round your answer to three decimal places.)
(d) What is P(A3|L)? (Round your answer to three decimal places.)
Explanation / Answer
A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 4% arrive after the guaranteed delivery time.
Suppose that 50% of the overnight parcels are sent by means of express mail service A2 and the remaining 10% are sent by means of A3. Of those sent by means of A2, only 1% arrived late, whereas 5% of the parcels handled by A3 arrived late.
(a)What is the probability that a randomly selected parcel arrived late? (Hint: A tree diagram should help.)
(b) Suppose that a randomly selected overnight parcel arrived late. What is the probability that the parcel was shipped using mail service A1? That is, what is the probability of A1 given L, denoted P(A1|L)? (Round your answer to three decimal places.)
(c) What is P(A2|L)? (Round your answer to three decimal places.)
(d) What is P(A3|L)? (Round your answer to three decimal places.)
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