You’re a logistics engineer for a manufacturer of hard seltzer. You use three different shipping companies (?1, ?2, ?3) to distribute seltzers. You contract with ?1 50% of the time, ?2 40% of the time, and ?3 10% of the time. Of those sent by ?1, 2% arrive after the guaranteed delivery time (late delivery). Similarly, 1% of those handled by ?2 arrive late, and 5% of shipments by ?3 arrive late. a. What is the probability that a randomly selected shipment arrived late? b. What is the probability that a randomly selected shipment was sent via ?1 and was late? c. If a randomly selected shipment arrived on time, what is the probability that it was not sent via ?1?

You’re a logistics engineer for a manufacturer of hard seltzer. You use three different shipping companies (?1, ?2, ?3) to distribute seltzers. You contract with ?1 50% of the time, ?2 40% of the time, and ?3 10% of the time. Of those sent by ?1, 2% arrive after the guaranteed delivery time (late delivery). Similarly, 1% of those handled by ?2 arrive late, and 5% of shipments by ?3 arrive late. a. What is the probability that a randomly selected shipment arrived late? b. What is the probability that a randomly selected shipment was sent via ?1 and was late? c. If a randomly selected shipment arrived on time, what is the probability that it was not sent via ?1?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

You’re a logistics engineer for a manufacturer of hard seltzer. You use three different shipping
companies (?1, ?2, ?3) to distribute seltzers. You contract with ?1 50% of the time, ?2 40% of
the time, and ?3 10% of the time. Of those sent by ?1, 2% arrive after the guaranteed delivery
time (late delivery). Similarly, 1% of those handled by ?2 arrive late, and 5% of shipments by ?3
arrive late.
a. What is the probability that a randomly selected shipment arrived late?
b. What is the probability that a randomly selected shipment was sent via ?1 and was late?
c. If a randomly selected shipment arrived on time, what is the probability that it was not
sent via ?1?

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