Reference no: EM132105675

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.

1. Suppose that one ingredient batch is selected at random from the batch produced. What is the probability that it is defective?
2. 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?