A car manufacturer purchases car batteries from two different suppliers A and B. Suppose supplier A provides 60% of the batteries and supplier B provides the rest. If 6% of all batteries from supplier A are defective and 4% of the batteries from supplier B are defective. Determine the probability that a randomly selected battery is not defective.
Solution: P(Selecting not a defective battery) =1- P(Selecting a defective battery) or P(Selecting a defective battery given A is defective) or P(selecting a defective battery given B is defective)
P(Selecting a defective battery) = (.6*.06)+(.4*.04) = 0.052 P(Selecting a defective battery given A is defective) = (.6*.06) = 0.036 p(Selecting a defective battery given B is defective) - (.4*.04) = 0.016
Therefore P(Selective a not defective battery is ) = 1 - (0.052+0.036+0.016) = 0.9284
Please let me know if this is correct. Please provide you comment and advice on my solution . I am a bit confused whether it is correct or not.