A lumber grading system is known to be defective 20% of the time. Normally, 20% of the lumber that passes through is rejected, but when it is defective, 50% of the pieces are rejected. In either case, pieces that are accepted are graded in the following manner:
- 20% #1 Grade; 70% #2 Grade; and 10% #3
Draw a tree diagram outlining each possible outcome. Please include all of the relevant probabilities as well as the probability for each outcome.
a) What is the probability of accepting a piece of lumber?
b) What is the probability of getting a #2 Grade piece?
c) What is the probability of accepting a piece of lumber, if it is known that the machine is not defective?