Find the following probabilities....... 1. Probability that contractor #1 sends

Question

Find the following probabilities....... 1. Probability that contractor #1 sends a good shipment. 2. Probability that contractor #1 sends a bad shipment. 3. Probability that contractor #2 sends a good shipment. 4. Probability that Contractor #2 sends a bad shipment. 5. Probability that a shipment is good and it came from Contractor #1. 6. Probability that a shipment is bad and it came from Contractor #1. 7. Probability that a shipment is good and it came from Contractor #2. 8. Probability that a shipment is bad and it came from Contractor #2. 9. Probability that any shipment is good. 10. Probability that any shipment is bad. 11. You are looking at a good shipment-Probability it came from Contractor #1 12. You are looking at a good shipment-Probability it came from Contractor #2 13. You are looking at a bad shipment-Probability it came from Contractor #1 14. You are looking at a bad shipment-Probability it came from Contractor#2

Explanation / Answer

Answer to each part with calc:

1. P( C1 sends good shipment) = 1-P(bad ) = 1-.05 = .95
2. P( C1 sends bad shipment) = P(bad) = .05
3. P( C2 sends good shipment) = 1-P(bad ) = 1-.10 = .90
4. P( C2 sends bad shipment) = P(bad) = .10
5. P( shipment is good, and it came from C1) = (.65*.95) .62
6. P( shipment is bad,and it came from C1) = (.65*.05)=.0325
7. P( shipment is good,and it came from C2) = (.35*.90)= .315
8. P( shipment is bad,and it came from C2) = (.35*.10) = .035
9. P( any shipment is good) = .65*.95 + .35*.90 = .9325
10.P( any shipment is bad) = .65*.05 + .35*.10= .0675
11. P( shipment is good, and it came from C1) = (.65*.95)/(.65*.95 + .35*.90) = .66
12. P( shipment is good,and it came from C2) = (.35*.90)/(.35*.90+.65*.95) = .34
13. P( shipment is bad,and it came from C1) = (.65*.05)/(.65*.05 + .35*.10) = .48
14. P( shipment is bad,and it came from C2) = (.35*.10)/(.35*.10+.65*.05)=.52

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