Keegan needs to choose a code for her safe. She is allowed to pick a code between 3 and 8 digits long (a “digit” is any of the numbers 0 through 9). Keegan wants to keep the code as short as possible while maintaining good security. What is the least number of digits Keegan can pick for her code so that a potential thief has no more than a 0.0001% chance of breaking into her safe on the first attempt?

On average, how many more hits will he get when he bats 100 times at home during the day as opposed to 100 times away at night?

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?

Why is it so easy to buy on impulse and overspend with a credit card? what could you do to counteract this tendency?