The sad state lottery requires you to select a sequence of four different numbers from 0 through 47. (Order is important.) You are a winner if your sequence agrees with that in the drawing, and you are a fool prize winner if your selection of numbers is correct, but in the wrong order. What is the probability of being a winner? (Enter your probabilities as fractions.) What is the probability of being a fool prize winner? What is the probability that you are either a winner or a fool prize winner?

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?