to improve the quality of its parts output from a rate 2% defective, a client firm has invested in a testing machine. this testing machine is only able to reject some of the defective output and allows some defectives to pass as up to standard. the probability of the output being rejected when it is not defective is 0.01 and the probability of not being rejected when it is defective is 0.003

a) draw a tree diagram that represent this situation

b) what is the probability of a part being defective and not being rejected

c) what is the probability that a randomly chosen part is rejected or defective

d) what is the probability that a part is defective given it is rejected