1.You have a screw-making machine that will successfully make a screw 99% of the time and 1% of the time makes a defective screw. Assume that each time the machine makes a screw is an independent event. [For parts (a)-(c)]

(a)Explain what it means for the events to be independent.

(b)What is the expected number of defective screws if you use the machine 100 times?

(c)What is the probability of observing at least one defective screw if you use the machine 100 times?

(d)For (d) assume that once the machine makes a defective screw all following screws are also defective. Under this setting, do you believe that your answer to (b) would stay the same, increase or decrease? Explain why.