Show all of your work. No credit will be given if there is nowork. Simplify if possible, unless noted.
Setup:
• Suppose the probability of a part being manufactured byMachine A is 0.4
• Suppose the probability that a part was manufactured byMachine A and the part is defective is 0.12
• Suppose the probability that a part was NOT manufactured byMachine A and the part IS defective is 0.14
Questions To Answer: 1. (2 pts) Find the probability that a partis defective given that it was made by Machine A.
2. (2 pts) Find the probability that a part is defective.
3. (4 pts) Are the states of a part being made by Machine A andbeing defective independent? Circle your answer and state yourreason. YES, they are independent NO, they are NOT independentReason:
4. (2 pts) Find the probability that Machine A produced aspecific part, given that the part was defective. Round your finalanswer to 2 decimals, if needed.
