Name: AT 610-602 (U. Müller-Harknett) .. UIN: 1|2|3.1 4 | 5 | 6 | r each problem

Question

Name: AT 610-602 (U. Müller-Harknett) .. UIN: 1|2|3.1 4 | 5 | 6 | r each problem a maximum of 10 points can be earned. ork your problems in the space provided. Show all work clearly. Justify your answers. Draw box around your final answer . Suppose that an online merchant uses two competing companies to ship its products, Acme Parcel (AP) and Speedy Deliveries (SD). Overall, 40% of shipments are made using AP and 60% using SD. Recently, 20% of all shipments have arrived late. AP seems to be more reliable than SD: shipments with AP are late with probability 0.1. Suppose a package was shipped using SD. Find the probability that it arrives late.

Explanation / Answer

Here we are given that:

P( AP ) = 0.4 and P( SD ) = 0.6

Also we are given that P( late ) = 0.2

Shipments with AP are late with a probability of 0.1. Therefore P( late | AP ) = 0.1

Now using the law of total probability, we get:

P( late ) = P( AP ) P( late | AP ) + P( SD ) P( late | SD )

Putting all the values, we get:

0.2 = 0.4*0.1 + 0.6*P( late | SD )

Therefore, we get:

P( late | SD ) = ( 0.2 - 0.04) / 0.6 = 0.2667

Therefore, given that the packaged arrived by SD, the probability that it was late is given as 0.2667

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

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