Joe knows that the additives used for creating his product is too dry 10% of the time and too wet 20% of the time, and has the correct amount of ingredients 70% of the time. He also knows that defective batches occur 20% of the time when the ingredient is too dry, 30% of the time when the ingredient is too wet and 5% of the time when the ingredient has the correct amount of ingredients.
- Suppose that one ingredient batch is selected at random from the batch produced. What is the probability that it is defective?
- Suppose one batch is selected at random and found to be defective. What is the conditional probability that it was too wet or too dry?