What is the probability that a randomly selected wiper is not defective? Use the

Question

What is the probability that a randomly selected wiper is not defective?

Use the following scenario and data for all questions The rain wipers installed on a specific model of SUVs are from four suppliers. The proportion of wipers provided by each supplier and the defective rate of each supplier for all four suppliers are listed in the following table. Use A, B, C or D to denote the event that a randomly selected wiper is from Supplier A, B, C or D respectively. Use Fto denote the event that a randomly selected wiper is defective Proportion Defective Rate 0.05 0.04 0.02 0.03 upplier 0.15 0.20 0.25 0.40 1.00 Total

Explanation / Answer

a) Probability that a randomly selected wiper is not defective is computed as:

= 1- Probability that a randomly selected wiper is defective

= 1 - P(A)*P(defective | A) - P(B)*P(defective | B) - P(C)*P(defective | C)- P(D)*P(defective | D)

= 1 - 0.15*0.05 - 0.2*0.04 - 0.25*0.02 - 0.4*0.03

= 1 - 0.0325

= 0.9675

Therefore the required probability here is 0.9675

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