SOLUTION: Suppose you work for a small company with delivery vans. The business has three drivers who deliver packages to private individuals. Driver 1 takes 30% of the runs but delivers

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Question 1183702: Suppose you work for a small company with delivery vans. The business has three drivers who deliver packages to private individuals.
Driver 1 takes 30% of the runs but delivers to the wrong address in 5% of the runs
Driver 2 takes 20% of the journeys but delivers to the wrong address in 2% of the journeys
Driver 3 takes 50% of the runs but delivers to the wrong address in 10% of the runs

1. What proportion of deliveries go to the right address?
2. What is the probability that the latest package that arrived at the correct address was delivered by Driver 3?
3. Assume that you have now received a complaint from a customer who has not received their package. What is the probability that that delivery would have been delivered by Driver 1?
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. P(correct address) = P(correct address AND driver 1) + P(correct address AND driver 2) + P(correct address AND driver 3) = 0.285 + 0.196 + 0.45 = highlight%280.931%29

***highlight%28Note%29: Compare the final answer with that of tutor ikleyn, whose final answer is 0.391, which is a mis-arrangment of digits of the correct final answer.
(Rather funny)


2. P(driver 3| correct address) = P(correct address AND driver 3)/P(correct address) = 0.45/0.931 = highlight%280.48335%29 (5 d.p.)

3. P(driver 1| wrong address) = P(wrong address AND driver 1)/P(wrong address) = 0.015/0.069 = highlight%280.21739%29 (5 d.p.)

Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
Suppose you work for a small company with delivery vans. The business has three drivers who deliver packages to private individuals.
Driver 1 takes 30% of the runs but delivers to the wrong address in 5% of the runs
Driver 2 takes 20% of the journeys but delivers to the wrong address in 2% of the journeys
Driver 3 takes 50% of the runs but delivers to the wrong address in 10% of the runs
1. What proportion of deliveries go to the right address?
2. What is the probability that the latest package that arrived at the correct address was delivered by Driver 3?
3. Assume that you have now received a complaint from a customer who has not received their package.
What is the probability that that delivery would have been delivered by Driver 1?
~~~~~~~~~~~~ 


(1)  P = 0.3*(1-0.05) + 0.2*(1-0.02) + 0.5*(1-0.1) = 0.3*0.95 + 0.2*0.98 + 0.5*0.9 = highlight%28cross%280.391%29%29  0.931  (fixing the typo).      ANSWER



(2)  This question in the post is formulated   I N C O R R E C T L Y.

     The correct formulation is as follows


          "What is the probability that a highlight%28cross%28latest%29%29 package that arrived at the correct address was delivered by Driver 3?


     The formula and the answer are  P = %280.5%2A0.9%29%2F%280.3%2A0.95+%2B+0.2%2A0.98+%2B+0.5%2A0.9%29 = 0.48335.      ANSWER



(3)  P = %280.3%2A0.05%29%2F%280.2%2A0.95+%2B+0.5%2A0.02+%2B+0.5%2A0.1%29 = 0.21739.      ANSWER

Solved.

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It is equally important to know how to write the general formulas in symbolic form (as tutor @robertb did)
and how to write the formulas in numerical form.

It is why I wrote my post.