Final answer:
To determine the probability that an iPhone is defective, calculate the weighted average of defect rates from each factory. Multiply each factory's production percentage by its defect rate and add them together. The total probability is 1.6%.
Step-by-step explanation:
The question is about calculating the probability of an iPhone being defective based on the production and defect rates in two different factories. We are given that factory one produces 40% of the iPhones and has a 1% defect rate, and factory two produces the remaining 60% of iPhones with a 2% defect rate. To find the overall probability of a defective iPhone, we must use the total probability formula which takes into account both the production rates and defect rates of each factory.
The formula for the total probability of a defective iPhone is:
P(Defective) = P(Defective|Factory 1) \(times P(Factory 1) + P(Defective|Factory 2) \(times P(Factory 2)
The probability that an iPhone from factory one is defective is 0.01, and from factory two is 0.02. Since 40% of iPhones come from factory one and the remaining 60% from factory two, we calculate as follows:
P(Defective) = (0.01 \(times 0.40) + (0.02 \(times 0.60) = 0.004 + 0.012 = 0.016
The overall probability that an iPhone will be defective is 1.6%.