Discussion Question 2 – (CLOs covered : 1, 2)
Horwege Electronics Inc. purchases TV picture tubes from four different suppliers. Tyson Wholesale supplies 20% of the tubes, Fuji Importers 30%, Kirkpatricks 25%, and Parts Inc. 25%. Tyson Wholesale tends to have the best quality, as only 3% of its tubes arrive defective. Fuji Importers’ tubes are 4% defective, Kirkpatricks’ 7%, and Parts Inc.’s are 6.5% defective.
a. What is the overall percent defective?
b. A defective picture tube was discovered in the latest shipment. What is the probability that it came from Tyson Wholesale?
In the second week of our course, we discussed three chapters among which probability is one of them. Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes’ relative likelihoods and distributions. This week 2 DQ 2 is mainly focused on the concepts of probability.
Numerical Calculations for Horwege Electronics Inc.
Given;
Name of the Suppliers | Supply Percentage (%) | Defective Percentage (%) |
Tyson Wholesale | 20% | 3% |
Fuji Importers | 30% | 4% |
Kirkpatricks | 25% | 7% |
Parts Inc. | 25% | 6.5% |
Working Notes:
- Probability of Tyson Wholesale supplying the tubes P(T)=20/100 = 0.2
- Probability of Fuji Importers supplying the tubes P(F) =30/100 = 0.3
- Probability of Kirkpatrick’s supplying the tubes P(K) = 25/100 = 0.25
- Probability of Parts Inc. supplying the tubes P(P) = 25/100 = 0.25
The probability of getting defective tubes for each supplier are;
- Tyson Wholesale supplier P(A|T)= 3/100 = 0.03
- Fuji Importers supplier P(A|F)= 4/100 = 0.04
- Kirkpatricks supplier P(A|K)= 7/100 = 0.07
- Parts Inc. supplier P(A|P)= 6.5/100 = 0.065
ANSWER A:
Overall defective percentage = P (T)*P(A|T) + P(F)*P(A|F) + P(K)*P(A|K) + P(P)*P(A|P)
= (0.2 x 0.03) + (0.3 x 0.04) + (0.25 x 0.07) + (0.25 x 0.065)
= 0.006 + 0.012 + 0.0175 + 0.01625
= 0.05175
= 5.175%
Therefore, the probability of overall defective percentage 5.175% out of 100%.
ANSWER B:
According to the question, a defective picture tube was discovered in the latest shipment.
Probability that it came from Tyson Wholesale
P(T|A) = {P(T) x P(A|T)} / {P(T) x P(A|T) + P(F) x P(A|F) + P(K) x P(A|K) + P(P) x P(A|P)}
= (0.2 x 0.03) / {(0.2 x 0.03) + (0.3 x 0.04) + (0.25 x 0.07) + (0.25 x 0.065)}
= 0.006 / (0.006 + 0.012 + 0.0175 + 0.01625)
= 0.006 / 0.05175
= 0.116
=11.6%
Therefore, the probability that it came from Tyson Wholesale is 11.6%.
