A manufacturer makes two models of an item: model A which accounts for 70% of unit sales, and model B which accounts for 30% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 4% of its model A and 17% of its model B.
Question 9 : If a unit is selected at random from the combined output, what is the probability that it will be defective?
To find the probability that a randomly selected unit will be defective, we need to consider the defect rates of both Model A and Model B and their respective proportions in unit sales.
Let's calculate the probability for each model individually and then combine them to get the overall probability.
1. Model A:
Since Model A accounts for 70% of unit sales and 4% of them are defective, we can calculate the probability of selecting a defective Model A unit.
Probability of selecting a defective Model A = 70% * 4% = 0.7 * 0.04 = 0.028 (or 2.8%)
2. Model B:
Similarly, as Model B accounts for 30% of unit sales and 17% of them are defective, we can calculate the probability of selecting a defective Model B unit.
Probability of selecting a defective Model B = 30% * 17% = 0.3 * 0.17 = 0.051 (or 5.1%)
3. Overall probability:
To find the overall probability of selecting a defective unit, we need to consider the proportions of Model A and Model B. The combined probability will be the weighted sum of the probabilities calculated above.
Overall probability of selecting a defective unit = (Probability of selecting a defective Model A * Proportion of Model A)
+ (Probability of selecting a defective Model B * Proportion of Model B)
Overall probability of selecting a defective unit = (0.028 * 70%) + (0.051 * 30%)
= 0.0196 + 0.0153
= 0.0349 (or 3.49%)
Therefore, the probability that a randomly selected unit from the combined output will be defective is 3.49%.
To find the probability that a randomly selected unit will be defective, we need to consider the defect rates for both model A and model B.
First, let's calculate the defect rate for model A:
Defect rate for model A = 70% of unit sales * 4% defect rate = 0.70 * 0.04 = 0.028.
Next, let's calculate the defect rate for model B:
Defect rate for model B = 30% of unit sales * 17% defect rate = 0.30 * 0.17 = 0.051.
Now, let's calculate the overall defect rate for the combined output:
Overall defect rate = defect rate for model A + defect rate for model B = 0.028 + 0.051 = 0.079.
Therefore, the probability that a randomly selected unit will be defective is 0.079, or 7.9%.