Let U represent the set of people in a certain community who were asked if they subscribe to an information source.

Let D ={ x ∈ U | x subscribes to The Daily Informer }
and
N ={ x ∈ U | x subscribes to News Magazine }

(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to The Daily Informer but not News Magazine.

a) D

b) ( N ∪ D )c

c) N c ∪ D

d) N c ∪ D c

e) N c ∩ D

f) None of the above.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?