The capulet and montague families love writing. last year, each capulet wrote 444 essays, each montague wrote 666 essays, and both families wrote 100100100 essays in total. this year, each capulet wrote 888 essays, each montague wrote 121212 essays, and both families wrote 200200200 essays in total. how many capulets and montagues are there? choose 1

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?